On the Extension of Ricci Harmonic Flow

Guoqiang Wu; Yu Zheng

doi:10.1007/s00025-020-1185-6

On the Extension of Ricci Harmonic Flow

Guoqiang Wu^*
, Yu Zheng

^*此作品的通讯作者

数学科学学院

Zhejiang Sci-Tech University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In this paper, we consider the extension problem of Ricci harmonic flow. On one hand, using the method of blowing up, we prove Ricci harmonic flow can be extended if Ln+22 norm of Riemannian curvature operator on M× [0 , T) is bounded. On the other hand, we establish L^∞ bound for nonnegative subsolution to linear parabolic equation, as an application, we prove that Ricci harmonic flow can be extended if Ln+22 norm of scalar curvature on M× [0 , T) is bounded and Ricci curvature has a uniform lower bound.

源语言	英语
文章编号	55
期刊	Results in Mathematics
卷	75
期	2
DOI	https://doi.org/10.1007/s00025-020-1185-6
出版状态	已出版 - 1 4月 2020

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abstract = "In this paper, we consider the extension problem of Ricci harmonic flow. On one hand, using the method of blowing up, we prove Ricci harmonic flow can be extended if Ln+22 norm of Riemannian curvature operator on M× [0 , T) is bounded. On the other hand, we establish L∞ bound for nonnegative subsolution to linear parabolic equation, as an application, we prove that Ricci harmonic flow can be extended if Ln+22 norm of scalar curvature on M× [0 , T) is bounded and Ricci curvature has a uniform lower bound.",

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AB - In this paper, we consider the extension problem of Ricci harmonic flow. On one hand, using the method of blowing up, we prove Ricci harmonic flow can be extended if Ln+22 norm of Riemannian curvature operator on M× [0 , T) is bounded. On the other hand, we establish L∞ bound for nonnegative subsolution to linear parabolic equation, as an application, we prove that Ricci harmonic flow can be extended if Ln+22 norm of scalar curvature on M× [0 , T) is bounded and Ricci curvature has a uniform lower bound.

KW - Ricci harmonic flow

KW - moser iteration

KW - sobolev constant

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On the Extension of Ricci Harmonic Flow

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