

Bibliography for
The Cauchy-Riemann
Equations
unabridged
- On
Maximal Sobolev and Holder Estimates for the Tangential
Cauchy-Riemann Operator and Boundary
Laplacian
Kenneth Douglas Koenig 1973-
American Journal of Mathematics, Vol. 124, No. 1. (Feb., 2002),
pp. 129-197, Jstor.
- Existence of Generalized Cauchy-Riemann Side-Systems in
Several Complex Variables
Hayashi Y.
Complex Variables, 1 October 2002, vol. 47, no. 10, pp.
881-889(9), Ingenta.
- Explicit methods for the solution of the generalized
Cauchy-Riemann equations and simulation of inviscid rotational
flows
Roy J.; Hafez M.; Chattot J.
J. Computers and Fluids, May 2002, vol. 31, no. 4, pp.
769-786(18), Ingenta.
- Robinson manifolds and Cauchy-Riemann spaces
Trautman A.
Classical and Quantum Gravity, 2002, vol. 19, no. 2, pp.
R1-R10(1), Ingenta.
- The Cauchy--Riemann Equations: Discretization by Finite
Elements, Fast Solution of the Second Variable, and a Posteriori
Error Estimation
Brandts J.
Advances in Computational Mathematics, November 2001, vol. 15, no.
1-4, pp. 61-77(17), Ingenta.
- On maps of CR manifolds and transformations of differential
equations
Alexandre Sukhov
Comptes Rendus de l'Académie des Sciences - Series I -
Mathematics, Volume 333, Issue 6, September 2001, Pages 545-550,
ScienceDirect.
- Équation de Cauchy--Riemann pour les courants
prolongeables -- applications
Salomon Sambou
Comptes Rendus de l'Académie des Sciences - Series I -
Mathematics, Volume 332, Issue 6, 15 March 2001, Pages 497-500,
ScienceDirect.
- Lp-curvature and the Cauchy-Riemann equation near an isolated
singular point.
Harris, Adam; Tonegawa, Yoshihiro
Nagoya Math. J. 164 (2001), 35--51, MathSciNet.
- Second microlocalization methods for degenerate Cauchy-Riemann
equations.
Lerner, Nicolas
Carleman estimates and applications to uniqueness and control
theory (Cortona, 1999), 109--128, Progr. Nonlinear Differential
Equations Appl., 46, Birkhäuser Boston, Boston, MA, 2001,
MathSciNet.
- On Symmetric Cauchy--Riemann Manifolds
Kaup W.; Zaitsev D.
Advances in Mathematics, February 2000, vol. 149, no. 2, pp.
145-181(37), Ingenta.
- A Remark on the Reduction of Cauchy-Riemann
Manifolds
Frank Loose
Mathematische Nachrichten, Volume: 214, Issue: 1, Date: June 2000,
Pages: 39-51, Wiley InterScience.
- Variétés Cauchy--Riemann homogènes et
enveloppes holomorphes
Karl Oeljeklaus and Christine Sacré
Bulletin des Sciences Mathématiques, Volume 124, Issue 3,
April 2000, Pages 193-211,
ScienceDirect.
- Convexité et équations de Cauchy-Riemann avec
estimations Lp. (French) [Convexity and Cauchy-Riemann
equations with Lp-estimates]
Jouenne, Corinne
Publ. Mat. 44 (2000), no. 1, 309--323,
MathSciNet.
- Simulation of steady compressible flows based on
Cauchy/Riemann equations and Crocco's relations. Part II. Viscous
flows
M. Hafez, W. Guo
Int. J. for Numerical Methods in Fluids, Volume: 31, Issue: 1,
Date: 15 September 1999, Pages: 325-343, Wiley
InterScience.
- Prolongement de courants positifsà travers une
sous-variété CR
Stéphane Giret
Journal des Mathématiques Pures et Appliqués, Volume
78, Issue 9, 9 November 1999, Pages 895-911,
ScienceDirect.
- Dolbeault isomorphism in CR manifolds
Christine Laurent-Thiébaut and Jürgen Leiterer
Comptes Rendus de l'Académie des Sciences - Series I -
Mathematics, Volume 328, Issue 6, 15 March 1999, Pages 469-472,
ScienceDirect.
- Optimal weighted estimates for the Cauchy-Riemann equation on
analytic polyhedra.
Cho, Hong Rae; Lee, Jinkee
Bull. Austral. Math. Soc. 59 (1999), no. 3, 427--431,
MathSciNet.
- Simulation of steady compressible flows based on
Cauchy/Riemann equations and Crocco's relation
M. Hafez, W. H. Guo
Int. J. for Numerical Methods in Fluids, Volume: 27, Issue: 1-4,
Date: January 1998, Pages: 127-138, Wiley
InterScience.
- Formules de représentation intégrale et
application à la résolution de l'équation de
Cauchy-Riemann dans le disque unité
généralisé de Mn(C). (French) [Integral
representation formulas and application to the solution of the
Cauchy-Riemann equation in the generalized unit disk of
Mn(C)]
Hachaichi, Mohamed-Salah
Maghreb Math. Rev. 7 (1998), no. 2, 101--134,
MathSciNet.
- The Cauchy Riemann equation on singular spaces.
Fornæss, John Erik; Gavosto, Estela A.
Duke Math. J. 93 (1998), no. 3, 453--477,
MathSciNet.
- Analysis
of the Cell Vertex Finite Volume Method for the Cauchy-Riemann
Equations
M. Vanmaele; K. W. Morton; E. Suli; A. Borzi
SIAM Journal on Numerical Analysis, Vol. 34, No. 5. (Oct., 1997),
pp. 2043-2062, Jstor.
- Cauchy-Riemann equations in a family of convex domains of
finite type
Corinne Jouenne
Comptes Rendus de l'Académie des Sciences - Series I -
Mathematics, Volume 325, Issue 9, November 1997, Pages 949-952,
ScienceDirect.
- On
CR-Mappings Between Algebraic Cauchy-Riemann Manifolds and
Separate Algebraicity for Holomorphic
Functions
Ruslan Sharipov; Alexander Sukhov
Transactions of the American Mathematical Society, Vol. 348, No.
2. (Feb., 1996), pp. 767-780, Jstor.
- Double-periodic solutions of nonlinear Cauchy-Riemann
equations
Sergei B. Kuksin
Communications on Pure and Applied Mathematics, Volume: 49, Issue:
7, Date: July 1996, Pages: 639-676, Wiley
InterScience.
- The Effect of a Nonlinear Viscous Regularization on the
Solution of a Cauchy--Riemann Equation
Anne C. Morlet
Journal of Mathematical Analysis and Applications, Volume 204,
Issue 1, 15 November 1996, Pages 236-282,
ScienceDirect.
- A successive approximation method for systems of nonlinear
Cauchy-Riemann equations. (Chinese)
Lü, De; Zeng, Yue Sheng
Huaihua Shizhuan Xuebao 13 (1994), no. 2, 9--12,
MathSciNet.
- Partial difference equations analogous to the Cauchy-Riemann
equations and related functional equations on rings and
fields.
Haruki, S.; Ng, C. T.
Results Math. 26 (1994), no. 3-4, 316--323,
MathSciNet.
- Uniform estimates for the Cauchy-Riemann equation on q-convex
wedges.
Laurent-Thiébaut, C.; Leiterer, J.
Ann. Inst. Fourier (Grenoble) 43 (1993), no. 2, 383--436,
MathSciNet.
- On
Three-Dimensional Cauchy-Riemann
Manifolds
Laszlo Lempert
Journal of the American Mathematical Society, Vol. 5, No. 4.
(Oct., 1992), pp. 923-969, Jstor.
- Hypoellipticity
on Cauchy-Riemann Manifolds
Johannes A. Petersen
Transactions of the American Mathematical Society, Vol. 334, No.
2. (Dec., 1992), pp. 615-639, Jstor.
- A fast algorithm to solve nonhomogeneous Cauchy-Riemann
equations in the complex plane.
Daripa, Prabir
SIAM J. Sci. Statist. Comput. 13 (1992), no. 6, 1418--1432,
MathSciNet.
- Elliptic
Differential Operators in Harmonic Analysis, I. Generalized
Cauchy-Riemann Systems
K. M. Davis; J. E. Gilbert; R. A. Kunze
American Journal of Mathematics, Vol. 113, No. 1. (Feb., 1991),
pp. 75-116, Jstor.
- Microlocal analysis of tangential systems of Cauchy-Riemann
equations. (Japanese)
Tajima, Shinichi
Sugaku 43 (1991), no. 2, 139--150, MathSciNet.
- Local homotopy formulas for the tangential Cauchy-Riemann
equations.
Trèves, F.
Partial differential equations and related subjects (Trento,
1990), 238--243, Pitman Res. Notes Math. Ser., 269, Longman Sci.
Tech., Harlow, 1992, MathSciNet.
- Solvability of the Cauchy-Riemann equation with constraints on
the growth of the functions, and weighted approximation of
analytic functions. (Russian)
Epifanov, O. V.
Izv. Vyssh. Uchebn. Zaved. Mat. 1990, , no. 2, 49--52; translation
in Soviet Math. (Iz. VUZ) 34 (1990), no. 2, 56--59,
MathSciNet.
- Yang-Mills fields, the Radon-Penrose transform and the
Cauchy-Riemann equations. (Russian) Current problems in
mathematics.
Novikov, R. G.; Khenkin, G. M.
Fundamental directions, Vol. 54 (Russian), 113--196, Itogi Nauki i
Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn.
Inform., Moscow, 1989, MathSciNet.
- A Bochner-Martinelli formula for vector fields which satisfy
the generalized Cauchy-Riemann equations.
Brummelhuis, R. G. M.
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), no. 4,
555--566 (1989), MathSciNet.
- Noethericity of generalized Cauchy-Riemann equations.
(Russian)
Mukhamadiev, È.; Baui zaev, S.
Izv. Akad. Nauk Tadzhik. SSR Otdel. Fiz.-Mat. Khim. i Geol. Nauk
1988, no. 2(108), 3--9, MathSciNet.
- Cauchy-Riemann equations in a class of quaternion functions.
(Russian)
Marinov, M. S.
Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat. 23 (1987), no. 2,
107--122 (1988), MathSciNet.
- Corona problems, interpolation problems, and inhomogeneous
Cauchy-Riemann equations.
Garnett, John B.
Proceedings of the International Congress of Mathematicians, Vol.
1, 2 (Berkeley, Calif., 1986), 917--923, Amer. Math. Soc.,
Providence, RI, 1987, MathSciNet.
- A
Comparative Study of Finite Element and Finite Difference Methods
for Cauchy-Riemann Type Equations
George J. Fix; Milton E. Rose
SIAM Journal on Numerical Analysis, Vol. 22, No. 2. (Apr., 1985),
pp. 250-261, Jstor.
- A
Kernel Approach to the Local Solvability of the Tangential Cauchy
Riemann Equations
A. Boggess; M.-C. Shaw
Transactions of the American Mathematical Society, Vol. 289, No.
2. (Jun., 1985), pp. 643-658, Jstor.
- Generalization of Cauchy--Riemann equations
A. K. Kwaniewski
Reports on Mathematical Physics, Volume 22, Issue 1, August 1985,
Pages 133-148, ScienceDirect.
- A multigrid method for the Cauchy-Riemann equations based on
flux-difference splitting and its extension to the steady Euler
equations
E. Dick
Journal of Computational and Applied Mathematics, Volumes 12-13,
May 1985, Pages 247-263,
ScienceDirect.
- The
partial-Neumann Solution to the Inhomogeneous Cauchy-Riemann
Equation in the Ball in C^n
F. Reese Harvey; John C. Polking
Transactions of the American Mathematical Society, Vol. 281, No.
2. (Feb., 1984), pp. 587-613, Jstor.
- On generalized Cauchy-Riemann equations on manifolds.
Proceedings of the 12th winter school on abstract analysis
(Srní, 1984).
Burevs, Jarolím; Souvcek, Vladimír
Rend. Circ. Mat. Palermo (2) 1984, Suppl. No. 6, 31--42,
MathSciNet.
- Integral representations on Hermitian manifolds: the
partial-Neumann solution of the Cauchy-Riemann equations.
Lieb, Ingo; Range, R. Michael
Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 2, 355--358,
MathSciNet.
- Tangent Cauchy-Riemann equations and the Yang-Mills, Higgs and
Dirac fields.
Henkin, G. M.
Proceedings of the International Congress of Mathematicians, Vol.
1, 2 (Warsaw, 1983), 809--827, PWN, Warsaw, 1984,
MathSciNet.
- Complex differential systems and tangential Cauchy-Riemann
equations. (Russian)
Abrosimov, A. V.
Mat. Sb. (N.S.) 122(164) (1983), no. 4, 419--434,
MathSciNet.
- An
Elementary Integral Solution Operator for the Cauchy-Riemann
Equations on Pseudoconvex Domains in
C^n
R. Michael Range
Transactions of the American Mathematical Society, Vol. 274, No.
2. (Dec., 1982), pp. 809-816, Jstor.
- Levi
Geometry and the Tangential Cauchy-Riemann Equations on a Real
Analytic Submanifold of C^n
Al Boggess
Transactions of the American Mathematical Society, Vol. 272, No.
1. (Jul., 1982), pp. 351-374, Jstor.
- Formules explicites pour les solutions de l'équation de
Cauchy-Riemann dans certain domaines. (French) [Explicit
formulas for solutions of the Cauchy-Riemann equation in certain
domains]
Hachaichi, M. S.
C. R. Acad. Bulgare Sci. 35 (1982), no. 10, 1337--1340,
MathSciNet.
- A
'Unified' Numerical Treatment of the Wave Equation and the
Cauchy-Riemann Equations
Milton E. Rose
SIAM Journal on Numerical Analysis, Vol. 18, No. 2. (Apr., 1981),
pp. 372-376, Jstor.
- Partial difference equations analogous to the Cauchy-Riemann
equations.
Aczél, J.; Haruki, S.
Funkcial. Ekvac. 24 (1981), no. 1, 95--102,
MathSciNet.
- Kernels
for the Tangential Cauchy-Riemann
Equations
Al Boggess
Transactions of the American Mathematical Society, Vol. 262, No.
1. (Nov., 1980), pp. 1-49, Jstor.
- Vector cross products, harmonic maps and the Cauchy-Riemann
equations.
Gray, Alfred
Harmonic maps (New Orleans, La., 1980), pp. 57--74, Lecture Notes
in Math., 949, Springer, Berlin-New York, 1982,
MathSciNet.
- A
Fast Cauchy-Riemann Solver
Michael Ghil; Ramesh Balgovind
Mathematics of Computation, Vol. 33, No. 146. (Apr., 1979), pp.
585-635, Jstor.
- Higher
Order Analogues to the Tangential Cauchy Riemann Equations for
Real Submanifolds of C^n with C.R.
Singularity
Gary Alvin Harris
Proceedings of the American Mathematical Society, Vol. 74, No. 1.
(Apr., 1979), pp. 79-86, Jstor.
- On the singularity set of complex functions satisfying the
Cauchy-Riemann equations.
Pelling, M. J.
Michigan Math. J. 26 (1979), no. 2, 225--229,
MathSciNet.
- Cauchy-Riemann Differential Equations in Classical
Hydrodynamics
Roy, S.
Int. J. of Math. Ed. in Sci. and Tech., (1979), V. 10, No. 2, p.
291.
- Global behavior of some tangential Cauchy-Riemann
equations.
Burns, Daniel M., Jr.
Partial differential equations and geometry (Proc. Conf., Park
City, Utah, 1977), pp. 51--56, Lecture Notes in Pure and Appl.
Math., 48, Dekker, New York, 1979, MathSciNet.
- When
is a Function that Satisfies the Cauchy-Riemann Equations
Analytic?
J. D. Gray; S. A. Morris
American Mathematical Monthly, Vol. 85, No. 4. (Apr., 1978), pp.
246-256, Jstor.
- The complex Frobenius theorem and uniqueness of solutions to
the tangential Cauchy-Riemann equations.
Hunt, L. R.
J. Differential Equations 27 (1978), no. 2, 214--223,
MathSciNet.
- Unique continuation for solutions to the induced
Cauchy-Riemann equations.
Hunt, L. R.; Polking, J. C.; Strauss, M. J.
J. Differential Equations 23 (1977), no. 3, 436--447,
MathSciNet.
- Is a function that satisfies the Cauchy-Riemann equations
necessarily analytic?
Disney, S. A. R.; Gray, J. D.; Morris, S. A.
Austral. Math. Soc. Gaz. 2 (1975), no. 3, 67--81,
MathSciNet.
- A formula and estimates for the solution of the tangential
Cauchy-Riemann equation. (Russian)
Romanov, A. V.
Dokl. Akad. Nauk SSSR 220 (1975), 532--535,
MathSciNet.
- Propagation of singularities for the Cauchy-Riemann
equations.
Kohn, J. J.
Complex analysis (Centro Internaz. Mat. Estivo, I Ciclo,
Bressanone, 1973) pp. 177--280. Edizioni Cremonese, Rome, 1974,
MathSciNet.
- Singular integrals and estimates for the Cauchy-Riemann
equations.
Stein, E. M.
Bull. Amer. Math. Soc. 79 (1973), 440--445,
MathSciNet.
- The
Tangential Cauchy-Riemann Complex on
Spheres
G. B. Folland
Transactions of the American Mathematical Society, Vol. 171.
(Sep., 1972), pp. 83-133, Jstor.
- Denson Complex characteristic coordinates and tangential
Cauchy-Riemann equations.
Andreotti, Aldo; Hill, C.
Ann. Scuola Norm. Sup. Pisa (3) 26 (1972), 299--324,
MathSciNet.
- Similarity principle of the generalized Cauchy-Riemann
equations for several complex variables.
Koohara, Akira
J. Math. Soc. Japan 23 (1971), 213--249,
MathSciNet.
- Removable
Sets for Pointwise Solutions of the Generalized Cauchy-Riemann
Equations
Victor L. Shapiro
The Annals of Mathematics, 2nd Ser., Vol. 92, No. 1. (Jul., 1970),
pp. 82-101, Jstor.
- Tangential Cauchy-Riemann equations and uniform
approximation.
Freeman, Michael
Pacific J. Math. 33 1970 101--108, MathSciNet.
- Cauchy-Riemann
Relations in n Dimensions (in Brief
Versions)
T. E. Phipps, Jr.
American Mathematical Monthly, Vol. 75, No. 8. (Oct., 1968), pp.
881-882, Jstor.
- Cauchy-Riemann equations in several variables.
Greenfield, S. J.
Ann. Scuola Norm. Sup. Pisa (3) 22 1968 275--314,
MathSciNet.
- Generalization
of the Cauchy-Riemann Equations and Representations of the
Rotation Group
E. M. Stein; G. Weiss
American Journal of Mathematics, Vol. 90, No. 1. (Jan., 1968), pp.
163-196, Jstor.
- A generalization of the Cauchy-Riemann equations.
Horváth, J.
Contributions to Differential Equations 1 1963 39--58,
MathSciNet.
- A generalisation of the Cauchy-Riemann equations and the
harmonicity of monogenic hypercomplex functions. (Russian)
Morev, I. A.
Izv. Vysvs. Uvcebn. Zaved. Matematika 1958 1958 no. 3 (4),
176--182, MathSciNet.
- From
Generalized Cauchy-Riemann Equations to Linear
Algebras
James A. Ward
Proceedings of the American Mathematical Society, Vol. 4, No. 3.
(Jun., 1953), pp. 456-461, Jstor.
- On a property of solutions of a generalized system of
Cauchy-Riemann equations. (Russian)
Vekua, I. N.
Soobvsvc. Akad. Nauk Gruzin. SSR 14 (1953), 449--453,
MathSciNet.
- On Cauchy-Riemann equations in higher dimensions.
Stiefel, E.
J. Research Nat. Bur. Standards 48, (1952). 395--398,
MathSciNet.
- A
Generalization of the Cauchy-Riemann
Equations
K. P. Williams
The Annals of Mathematics, 2nd Ser., Vol. 30, No. 1/4. (1928 -
1929), pp. 206-210, Jstor.
- Concerning
Green's Theorem and the Cauchy-Riemann Differential
Equations
M. B. Porter
The Annals of Mathematics, 2nd Ser., Vol. 7, No. 1. (Oct., 1905),
pp. 1-2, Jstor.
Return
to the Complex Analysis Project
(c) John
H. Mathews 2003