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Journal of Evolution Equations

, Volume 18, Issue 4, pp 1595–1632 | Cite as

The Yamabe flow on incomplete manifolds

  • Yuanzhen Shao
Article
  • 21 Downloads

Abstract

This article is concerned with developing an analytic theory for second-order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an \(L_p\)-framework are established by maximal regularity tools. These techniques are applied to the Yamabe flow. It is proven that the Yamabe flow admits a unique local solution within a class of incomplete initial metrics.

Keywords

Singular parabolic equations Maximal \(L_p\)-regularity Incomplete Riemannian manifolds Geometric evolution equations The Yamabe flow 

Mathematics Subject Classification

35K55 35K67 35R01 53C21 53C44 58J99 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesGeorgia Southern UniversityStatesboroUSA

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