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Nirenberg's contributions to complex analysis
1. | Princeton University, Mathematics Department, Princeton, NJ 08544, United States |
References:
[1] |
T. Akahori, "A New Approach to the Local Embedding Theorem of CR-Structure for $n\ge4$,'' Memoirs of the A.M.S., Providence, RI, 1987. |
[2] |
S. Bell and E. Ligocka, A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math., 57 (1980), 283-289.
doi: 10.1007/BF01418930. |
[3] |
J. Bokobza and A. Unterberger, Les operators de Calderón-Zygmund précisés, C. R. Acad. Sci. Paris, 259 (1964), 1612-1614. |
[4] |
L. Caffarelli, J. J. Kohn, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, II: Complex Monge-Ampère, and uniformly elliptic equations, Comm. Pure Appl. Math., 38 (1985), 209-252.
doi: 10.1002/cpa.3160380206. |
[5] |
D. Catlin, Necessary conditions for subellipticity of the $\bar\partial$-Neumann problem, Ann. of Math., 117 (1983), 147-171.
doi: 10.2307/2006974. |
[6] |
D. Catlin, Subelliptic estimates for the $\bar\partial$-Neumann problem on pseudoconvex domains, Ann. of Math., 126 (1987), 131-191.
doi: 10.2307/1971347. |
[7] |
S. S. Chern, H. I. Levine and L. Nirenberg, Intrinsic norms on a complex manifold, Global Anal., Univ. of Tokyo Press, (1969), 119-139. |
[8] |
S.-C. Chen and M.-C. Shaw, "Partial Differential Equations in Several Complex Variables," AMS/IP Stud. Adv. Math. 19, AMS Providence, R. I., 2001. |
[9] |
J. P. D'Angelo, Finite type conditions for real hypersurfaces, J. Diff. Geom., 14 (1979), 59-66. |
[10] |
C. L. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math., 26 (1974), 1-65.
doi: 10.1007/BF01406845. |
[11] |
G. Fichera, Sulle equazioni differenziali lineari ellitico-paraboliche del secondo ordine, Atti Acc. Naz. Lincei Mem. Ser. 8, 5 (1956), 97-120. |
[12] |
K. Kodaira, L. Nirenberg and D. C. Spencer, On the existence of deformations of complex analytic structures, Ann. of Math., 68 (1958), 450-459.
doi: 10.2307/1970256. |
[13] |
J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds I and II, Ann. of Math. 78 (1963), 112-148; 79 (1964), 450-472. |
[14] |
J. J. Kohn, Boundary behavior of $\bar\partial$ on weakly pseudo-convex manifolds of dimension two, J. Diff. Geom., 6 (1972), 523-542. |
[15] |
J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math., 18 (1965), 443-492.
doi: 10.1002/cpa.3160180305. |
[16] |
J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math., 18 (1965), 269-305.
doi: 10.1002/cpa.3160180121. |
[17] |
J. J. Kohn and L. Nirenberg, Degenerate ellptic-parabolic equations of second order, Comm. Pure Appl. Math., 20 (1967), 797-782.
doi: 10.1002/cpa.3160200410. |
[18] |
J. J. Kohn and L. Nirenberg, A pseudo-convex domain not admitting a holomorphic support function, Math. Ann., 201 (1973), 265-268.
doi: 10.1007/BF01428194. |
[19] |
M. Kuranishi, Strongly psedoconvex CR structures over small balls, Part I, An a priori estimate, Part II, A regularity theorem, Part III, An embedding theorem, Ann. of Math., 115 (1982), 451-500; 116 (1982), 1-64; 116 (1982), 249-330. |
[20] |
P. D. Lax and L. Nirenberg, On stability for difference schemes: A sharp form of Gårding's inequality, Comm. Pure Appl. Math., 19 (1966), 473-492.
doi: 10.1002/cpa.3160190409. |
[21] |
C. B. Morrey, The analytic embedding of abstract real analytic manifolds, Ann. of Math., 40 (1958), 62-70. |
[22] |
A. Newlander and L. Nirenberg, Complex analytic coordinates in almost complex manifolds, Ann. of Math., 65 (1957), 391-404.
doi: 10.2307/1970051. |
[23] |
L. Nirenberg, "A Complex Frobenius Theorem," Proc. Conf. Analytic Functions, vol. 1, Institute for Advanced Study, Princeton (1957), 172-189. |
[24] |
L. Nirenberg, On a question of Hans Lewy, Russian Math. Surveys, 29 (1974), 251-262. |
[25] |
L. Nirenberg and D. C. Spencer, On rigidity of holomorphic imbeddings, Contributions to function theory, Tata Institute of Fundamental Research, Bombay, (1960), 133-137. |
[26] |
L. Nirenberg, S. Webster and P. Yang, Local boundary regularity of holomorphic mappings, Comm Pure and Appl. Math., 33 (1980), 305-338.
doi: 10.1002/cpa.3160330306. |
[27] |
O. A. Oleinik, A boundary value problem for linear elliptic parabolic equations, Doklady Akad. Nauk. SSSR, 163 (1963), 577-580. |
[28] |
E. J. Straube, "Lectures on the $\mathcal L^2$-Sobolev Theory of the $\bar\partial$-Neumann Problem,'' LSI Lectures in Mathematics and Physics, European Mathematical Society, 2010.
doi: 10.4171/076. |
show all references
References:
[1] |
T. Akahori, "A New Approach to the Local Embedding Theorem of CR-Structure for $n\ge4$,'' Memoirs of the A.M.S., Providence, RI, 1987. |
[2] |
S. Bell and E. Ligocka, A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math., 57 (1980), 283-289.
doi: 10.1007/BF01418930. |
[3] |
J. Bokobza and A. Unterberger, Les operators de Calderón-Zygmund précisés, C. R. Acad. Sci. Paris, 259 (1964), 1612-1614. |
[4] |
L. Caffarelli, J. J. Kohn, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, II: Complex Monge-Ampère, and uniformly elliptic equations, Comm. Pure Appl. Math., 38 (1985), 209-252.
doi: 10.1002/cpa.3160380206. |
[5] |
D. Catlin, Necessary conditions for subellipticity of the $\bar\partial$-Neumann problem, Ann. of Math., 117 (1983), 147-171.
doi: 10.2307/2006974. |
[6] |
D. Catlin, Subelliptic estimates for the $\bar\partial$-Neumann problem on pseudoconvex domains, Ann. of Math., 126 (1987), 131-191.
doi: 10.2307/1971347. |
[7] |
S. S. Chern, H. I. Levine and L. Nirenberg, Intrinsic norms on a complex manifold, Global Anal., Univ. of Tokyo Press, (1969), 119-139. |
[8] |
S.-C. Chen and M.-C. Shaw, "Partial Differential Equations in Several Complex Variables," AMS/IP Stud. Adv. Math. 19, AMS Providence, R. I., 2001. |
[9] |
J. P. D'Angelo, Finite type conditions for real hypersurfaces, J. Diff. Geom., 14 (1979), 59-66. |
[10] |
C. L. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math., 26 (1974), 1-65.
doi: 10.1007/BF01406845. |
[11] |
G. Fichera, Sulle equazioni differenziali lineari ellitico-paraboliche del secondo ordine, Atti Acc. Naz. Lincei Mem. Ser. 8, 5 (1956), 97-120. |
[12] |
K. Kodaira, L. Nirenberg and D. C. Spencer, On the existence of deformations of complex analytic structures, Ann. of Math., 68 (1958), 450-459.
doi: 10.2307/1970256. |
[13] |
J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds I and II, Ann. of Math. 78 (1963), 112-148; 79 (1964), 450-472. |
[14] |
J. J. Kohn, Boundary behavior of $\bar\partial$ on weakly pseudo-convex manifolds of dimension two, J. Diff. Geom., 6 (1972), 523-542. |
[15] |
J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math., 18 (1965), 443-492.
doi: 10.1002/cpa.3160180305. |
[16] |
J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math., 18 (1965), 269-305.
doi: 10.1002/cpa.3160180121. |
[17] |
J. J. Kohn and L. Nirenberg, Degenerate ellptic-parabolic equations of second order, Comm. Pure Appl. Math., 20 (1967), 797-782.
doi: 10.1002/cpa.3160200410. |
[18] |
J. J. Kohn and L. Nirenberg, A pseudo-convex domain not admitting a holomorphic support function, Math. Ann., 201 (1973), 265-268.
doi: 10.1007/BF01428194. |
[19] |
M. Kuranishi, Strongly psedoconvex CR structures over small balls, Part I, An a priori estimate, Part II, A regularity theorem, Part III, An embedding theorem, Ann. of Math., 115 (1982), 451-500; 116 (1982), 1-64; 116 (1982), 249-330. |
[20] |
P. D. Lax and L. Nirenberg, On stability for difference schemes: A sharp form of Gårding's inequality, Comm. Pure Appl. Math., 19 (1966), 473-492.
doi: 10.1002/cpa.3160190409. |
[21] |
C. B. Morrey, The analytic embedding of abstract real analytic manifolds, Ann. of Math., 40 (1958), 62-70. |
[22] |
A. Newlander and L. Nirenberg, Complex analytic coordinates in almost complex manifolds, Ann. of Math., 65 (1957), 391-404.
doi: 10.2307/1970051. |
[23] |
L. Nirenberg, "A Complex Frobenius Theorem," Proc. Conf. Analytic Functions, vol. 1, Institute for Advanced Study, Princeton (1957), 172-189. |
[24] |
L. Nirenberg, On a question of Hans Lewy, Russian Math. Surveys, 29 (1974), 251-262. |
[25] |
L. Nirenberg and D. C. Spencer, On rigidity of holomorphic imbeddings, Contributions to function theory, Tata Institute of Fundamental Research, Bombay, (1960), 133-137. |
[26] |
L. Nirenberg, S. Webster and P. Yang, Local boundary regularity of holomorphic mappings, Comm Pure and Appl. Math., 33 (1980), 305-338.
doi: 10.1002/cpa.3160330306. |
[27] |
O. A. Oleinik, A boundary value problem for linear elliptic parabolic equations, Doklady Akad. Nauk. SSSR, 163 (1963), 577-580. |
[28] |
E. J. Straube, "Lectures on the $\mathcal L^2$-Sobolev Theory of the $\bar\partial$-Neumann Problem,'' LSI Lectures in Mathematics and Physics, European Mathematical Society, 2010.
doi: 10.4171/076. |
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