The interior regularity of the Calabi flow on a toric surface

Xiuxiong Chen; Hongnian Huang; Li Sheng

doi:10.1007/s00526-016-1028-1

The interior regularity of the Calabi flow on a toric surface

Xiuxiong Chen
, Hongnian Huang
, Li Sheng

Mathematics

University of New Mexico
Sichuan University

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

1 Scopus citations

Abstract

Let X be a toric surface with Delzant polygon P and u(t) be a solution of the Calabi flow equation on P. Suppose the Calabi flow exists in [0, T). By studying local estimates of the Riemann curvature and the geodesic distance under the Calabi flow, we prove a uniform interior estimate of u(t) for t< T.

Original language	English
Article number	106
Journal	Calculus of Variations and Partial Differential Equations
Volume	55
Issue number	4
DOIs	https://doi.org/10.1007/s00526-016-1028-1
State	Published - Aug 1 2016

Keywords

53C44
53C55

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10.1007/s00526-016-1028-1

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abstract = "Let X be a toric surface with Delzant polygon P and u(t) be a solution of the Calabi flow equation on P. Suppose the Calabi flow exists in [0, T). By studying local estimates of the Riemann curvature and the geodesic distance under the Calabi flow, we prove a uniform interior estimate of u(t) for t< T.",

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AU - Huang, Hongnian

AU - Sheng, Li

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N2 - Let X be a toric surface with Delzant polygon P and u(t) be a solution of the Calabi flow equation on P. Suppose the Calabi flow exists in [0, T). By studying local estimates of the Riemann curvature and the geodesic distance under the Calabi flow, we prove a uniform interior estimate of u(t) for t< T.

AB - Let X be a toric surface with Delzant polygon P and u(t) be a solution of the Calabi flow equation on P. Suppose the Calabi flow exists in [0, T). By studying local estimates of the Riemann curvature and the geodesic distance under the Calabi flow, we prove a uniform interior estimate of u(t) for t< T.

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DO - 10.1007/s00526-016-1028-1

M3 - Article

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

M1 - 106

ER -

The interior regularity of the Calabi flow on a toric surface

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