Subharmonic functions on real and complex manifolds

DOI10.1007/BF01215065zbMath0441.31005MaRDI QIDQ1142901

Leon Karp

Publication date: 1982

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173165

zbMATH Keywords

harmonic functionscurvature estimatesharmonic mappingsubharmonic functionsholomorphic mappingLiouville-type theoremsparabolic Riemannian manifold

Mathematics Subject Classification ID

Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Potential theory on Riemannian manifolds and other spaces (31C12)

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Cites Work

• Unnamed Item
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• Function theory on manifolds which possess a pole
• On subharmonic functions and differential geometry in the large
• Riemannsche Flächen von hyperbolischem Typus im euklidischen Raum
• On Kähler manifolds of positive bisectional curvature and a theorem of Hartogs
• Harmonic mappings and minimal submanifolds
• Asymptotic behavior of solutions of elliptic equations. I: Liouville-type theorems for linear and nonlinear equations on \(R^ n\).
• Asymptotic behavior of solutions of elliptic equations. II: Analogues of Liouville's theorem for solutions of inequalities on \(R^ n\), \(n\geq 3\)
• Integrals of subharmonic functions on manifolds of nonnegative curvature
• An existence theorem for harmonic mappings of Riemannian manifolds
• Complete Kähler manifolds with nonpositive curvature of faster than quadratic decay
• \(C^\infty\) convex functions and manifolds of positive curvature
• An elementary method in the study of nonnegative curvature
• Curvatures of complex submanifolds of \(C^n\)
• Carleman estimates for the Laplace-Beltrami equation on complex manifolds
• Stetige streng pseudokonvexe Funktionen
• A note on curvature and fundamental group
• On complete open manifolds of positive curvature
• Riemann Surfaces of Class A
• A Hyperbolic Surface in 3-Space
• The conservation property of the heat equation on riemannian manifolds
• On Stokes' Theorem for Noncompact Manifolds
• Approximation theorems, 𝐶^{∞} convex exhaustions and manifolds of positive curvature
• Differential equations on riemannian manifolds and their geometric applications
• On Deciding Whether a Surface is Parabolic or Hyperbolic
• Some properties and applications of harmonic mappings
• A Report on Harmonic Maps
• Manifolds of Negative Curvature
• Convex Functions and Harmonic Maps
• Curvature and complex analysis. II
• Harmonic Mappings of Riemannian Manifolds

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