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arXiv · 1506.07018

The Yamabe flow on incomplete manifolds

Yuanzhen Shao
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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 Lp-framework is 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.

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Yuanzhen Shao. 2015-06-23. The Yamabe flow on incomplete manifolds. https://doi.org/10.1007/s00028-018-0453-3

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