Diameter Estimate in Geometric Flows

Shouwen Fang; Tao Zheng

doi:10.3390/math11224659

Diameter Estimate in Geometric Flows

Shouwen Fang, Tao Zheng^*

^*Corresponding author for this work

School of Mathematics and Statistics

Yangzhou University

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

Abstract

We prove the upper and lower bounds of the diameter of a compact manifold (Formula presented.) with (Formula presented.) and a family of Riemannian metrics (Formula presented.) satisfying some geometric flows. Except for Ricci flow, these flows include List–Ricci flow, harmonic-Ricci flow, and Lorentzian mean curvature flow on an ambient Lorentzian manifold with non-negative sectional curvature.

Original language	English
Article number	4659
Journal	Mathematics
Volume	11
Issue number	22
DOIs	https://doi.org/10.3390/math11224659
Publication status	Published - Nov 2023

Keywords

diameter bound
geometric flow
heat kernel

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10.3390/math11224659

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Fang, S., & Zheng, T. (2023). Diameter Estimate in Geometric Flows. Mathematics, 11(22), Article 4659. https://doi.org/10.3390/math11224659

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abstract = "We prove the upper and lower bounds of the diameter of a compact manifold (Formula presented.) with (Formula presented.) and a family of Riemannian metrics (Formula presented.) satisfying some geometric flows. Except for Ricci flow, these flows include List–Ricci flow, harmonic-Ricci flow, and Lorentzian mean curvature flow on an ambient Lorentzian manifold with non-negative sectional curvature.",

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AB - We prove the upper and lower bounds of the diameter of a compact manifold (Formula presented.) with (Formula presented.) and a family of Riemannian metrics (Formula presented.) satisfying some geometric flows. Except for Ricci flow, these flows include List–Ricci flow, harmonic-Ricci flow, and Lorentzian mean curvature flow on an ambient Lorentzian manifold with non-negative sectional curvature.

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KW - heat kernel

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Diameter Estimate in Geometric Flows

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Keywords

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