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The Journal of Geometric Analysis

, Volume 29, Issue 2, pp 1649–1659 | Cite as

A Note on Existence of Exhaustion Functions and Its Applications

  • Shaochuang HuangEmail author
Article
  • 62 Downloads

Abstract

In this note, we use harmonic coordinates to prove an existence result on exhaustion functions by adapting the method in Tam (in: Recent Advances in Geometric Analysis, Advanced Lectures in Mathematics, vol. 11, pp. 211–215, International Press, Somerville, 2010). Then we apply it to prove short-time existence of Ricci flow using similar method in He (Existence and applications of Ricci flows via pseudolocality, arXiv:1610.01735) and Lee and Tam (On existence and curvature estimates of Ricci flow, arXiv:1702.02667) .

Keywords

Exhaustion function Short-time existence of Ricci flow Harmonic radius estimate 

Mathematics Subject Classification

Primary 53C21 Secondary 53C44 

Notes

Acknowledgements

The author would like to thank Mr. Pak-Yeung Chan for some helpful discussions and thank Professors Luen-Fai Tam, Guoyi Xu, Fei He and Mr. Man-Chun Lee for their interests in this work and some useful comments.

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Yau Mathematical Sciences CenterTsinghua UniversityBeijingChina

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