본문 바로가기
KERD
논문KCI 등재

Montel type theorem for CR mappings between pseudo-Hermitian CR manifolds

이한진
대한수학회 (The Korean Mathematical Society)|2024.09|대한수학회보 (Bulletin of the KMS)|제61권 제5호|pp. 1289-1299|DOI 10.4134/BKMS.b230540

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Normal familypseudo-hermitian manifoldsCR maps
주제분류수학

초록

Montel type theorem for CR mappings between strongly \linebreak pseudoconvex psuedo-Hermitian CR manifolds satisfying curvature bound conditions is proved. Pre-compactness relies on recently introduced \linebreak Schwarz lemma for CR mappings between pseudo-Hermitian manifolds. Smoothness of the limit CR map is proved using CR and holomorphic extensions of CR functions to higher dimensional q-concave CR manifolds.

Abstract

Montel type theorem for CR mappings between strongly \linebreak pseudoconvex psuedo-Hermitian CR manifolds satisfying curvature bound conditions is proved. Pre-compactness relies on recently introduced \linebreak Schwarz lemma for CR mappings between pseudo-Hermitian manifolds. Smoothness of the limit CR map is proved using CR and holomorphic extensions of CR functions to higher dimensional q-concave CR manifolds.

참고문헌 (15)

  1. R. A. Airapetyan, "Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR functions", Russian Math. Surv, 39, pp.41~118 (1984)
  2. M. Y. Barkatou, "Optimal regularity for ∂b on CR manifolds", J. Geom. Anal, 10(2), pp.219~241 (2000)[DOI]
  3. Y. -J. Choi, "Uniqueness theorems for CR and conformal mappings", Pacific J. Math, 258(2), pp.257~268 (2012)[DOI]
  4. Y. Dong, "Schwarz type lemmas for pseudo-Hermitian manifolds", J. Geom. Anal, 31(3), pp.3161~3195 (2021)[DOI]
  5. B. Fischer, "Kernels of Martinelli-Bochner type on hypersurfaces", Math. Z, 223(1), pp.155~183 (1996)[DOI]
  6. R. E. Greene, "The Geometry of Complex Domains" (2011), Birkhauser Boston, Ltd
  7. R. E. Greene, "Normal families and the semicontinuity of isometry and automorphism groups", Math. Z, 190(4), pp.455~467 (1985)[DOI]
  8. S. Kobayashi, "Hyperbolic Manifolds and Holomorphic Mappings" (2005), World Sci. Publ
  9. J. J. Kohn, "Estimates for ¯∂b on pseudoconvex CR manifolds, Pseudodifferential operators and applications", Proc. Sympos. Pure Math., 43, pp.207~217 (1985), Amer. Math. Soc
  10. B. Lamel, "A C∞-regularity theorem for nondegenerate CR mappings", Monatsh. Math, 142(4), pp.315~326 (2004)
  11. S. I. Pinchuk, "Smoothness of CR mappings of strongly pseudoconvex hypersurfaces", Akad. Nauk SSSR, 53, pp.1120~1129 (1989)
  12. R. Schoen, "On the conformal and CR automorphism groups", Geom. Funct. Anal, 5(2), pp.464~481 (1995)[DOI]
  13. M. -C. Shaw, "L2-estimates and existence theorems for the tangential Cauchy Riemann complex", Invent. Math, 82(1), pp.133~150 (1985)[DOI]
  14. S. K. Vodopyanov, "Geometry of Carnot-Carath´eodory spaces and differentiability of mappings, The Interaction of Analysis and Geometry", pp.247~301 (2007), Amer. Math. Soc
  15. H. Wu, "Normal families of holomorphic mappings", Acta Math, 119, pp.193~233 (1967)[DOI]

관련 논문AI추천

Nullity of the Levi-form and the associated subvarieties for pseudo-convex CR structures of hypersurface type정규락, 한종규대한수학회 · 대한수학회보2019 · 제56권 제1호Rigidity of proper holomorphic maps from B^(n+1) to B^(3n-1)왕승호대한수학회 · 대한수학회지2009 · 제46권 제5호Finiteness of infinitesimal deformationsof CR mappings of CR manifolds of nondegenerate Levi form조정기, 한종규대한수학회 · 대한수학회지2002 · 제39권 제1호Sobolev estimates for the local extension of boundary holomorphic forms on real hypersurfaces in Cn조상현대한수학회 · 대한수학회지2013 · 제50권 제3호HIGHER ORDER ASYMPTOTIC BEHAVIOR OF CERTAIN K¨ AHLER METRICS AND UNIFORMIZATION FOR STRONGLY PSEUDOCONVEX DOMAINS서애령, 주재천대한수학회 · 대한수학회지2015 · 제52권 제1호A bound on H\"older regularity for $\overline \partial$-equation on pseudoconvex domains in $\mathbb C^n$ with some comparable eigenvalues of the Levi-form조상현대한수학회 · 대한수학회보2021 · 제58권 제3호

이 간행물의 다른 논문 (14건)

Nonlinear Complexity And Weierstrass Semigroup Of Two Rational Points On A Hermitian CurveFerruh Ozbudak, Nesrin Tutaspp. 1161-1173A CLASSIFICATION OF REGULAR t-BALANCED CAYLEY MAPS ON Z2-EXTENSIONS OF A CYCLIC 2-GROUP박지혜, 권영수pp. 1175-1195An upper bound of the minimal asymptotic translation length of right-angled Artin groups on extension graphsEon-Kyung Lee, 이상진pp. 1197-1209Some results for $U$-statistics and strong demimartingalesXiaomei Zhang, Decheng Fengpp. 1211-1221Nonnil-P-coherent rings and nonnil-PP-rings김환구, El Houssaine Oubouhou, Najib Mahdoupp. 1223-1240
원문 보기