On the [InlineEquation not available: see fulltext.] Regularity of Geodesics in the Space of Kähler Metrics

Jianchun Chu; Valentino Tosatti; Ben Weinkove

doi:10.1007/s40818-017-0034-8

On the [InlineEquation not available: see fulltext.] Regularity of Geodesics in the Space of Kähler Metrics

Jianchun Chu, Valentino Tosatti, Ben Weinkove

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that any two Kähler potentials on a compact Kähler manifold can be connected by a geodesic segment of C^{1 , 1} regularity. This follows from an a priori interior real Hessian bound for solutions of the nondegenerate complex Monge-Ampère equation, which is independent of a positive lower bound for the right hand side.

Original language	English (US)
Article number	15
Journal	Annals of PDE
Volume	3
Issue number	2
DOIs	https://doi.org/10.1007/s40818-017-0034-8
State	Published - Dec 1 2017

Keywords

Complex Monge-Ampere equation
Geodesics in the space of Kahler metrics
Real Hessian estimates

ASJC Scopus subject areas

Analysis
Applied Mathematics
Geometry and Topology
Mathematical Physics
General Physics and Astronomy

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10.1007/s40818-017-0034-8

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abstract = "We prove that any two K{\"a}hler potentials on a compact K{\"a}hler manifold can be connected by a geodesic segment of C1 , 1 regularity. This follows from an a priori interior real Hessian bound for solutions of the nondegenerate complex Monge-Amp{\`e}re equation, which is independent of a positive lower bound for the right hand side.",

keywords = "Complex Monge-Ampere equation, Geodesics in the space of Kahler metrics, Real Hessian estimates",

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AU - Tosatti, Valentino

AU - Weinkove, Ben

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N2 - We prove that any two Kähler potentials on a compact Kähler manifold can be connected by a geodesic segment of C1 , 1 regularity. This follows from an a priori interior real Hessian bound for solutions of the nondegenerate complex Monge-Ampère equation, which is independent of a positive lower bound for the right hand side.

AB - We prove that any two Kähler potentials on a compact Kähler manifold can be connected by a geodesic segment of C1 , 1 regularity. This follows from an a priori interior real Hessian bound for solutions of the nondegenerate complex Monge-Ampère equation, which is independent of a positive lower bound for the right hand side.

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KW - Real Hessian estimates

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On the [InlineEquation not available: see fulltext.] Regularity of Geodesics in the Space of Kähler Metrics

Abstract

Keywords

ASJC Scopus subject areas

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