\(C^\infty\) convex functions and manifolds of positive curvature

DOI10.1007/BF02392418zbMath0372.53019WikidataQ125574673 ScholiaQ125574673MaRDI QIDQ1244527

Robert E. Greene, Hung-Hsi Wu

Publication date: 1977

Published in: Acta Mathematica (Search for Journal in Brave)

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Real-valued functions on manifolds (58C05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten
• On Levi's problem and the imbedding of real-analytic manifolds
• Some results on nonnegatively curved manifolds
• A generalized Allendoerfer-Weil formula and an inequality of the Cohn-Vossen type
• Integrals of subharmonic functions on manifolds of nonnegative curvature
• The Levi problem for complex spaces. II
• Stetige streng pseudokonvexe Funktionen
• Minimal varieties in Riemannian manifolds
• On complete open manifolds of positive curvature
• Toward a generalized Gauss-Bonnet formula for complete, open manifolds
• On the structure of complete manifolds of nonnegative curvature
• A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds
• Approximation theorems, 𝐶^{∞} convex exhaustions and manifolds of positive curvature
• Positive Sectional Curvatures Does not Imply Positive Gauss-Bonnet Integrand
• On Geroch's Counterexample to the Algebraic Hopf Conjecture
• Curvature and complex analysis
• The Gauss-Bonnet Theorem for Riemannian Polyhedra

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