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Yamabe flow on manifolds with edges
Author(s) -
Bahuaud Eric,
Vertman Boris
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200210
Subject(s) - mathematics , yamabe flow , singularity , flow (mathematics) , manifold (fluid mechanics) , operator (biology) , mathematical analysis , enhanced data rates for gsm evolution , class (philosophy) , riemannian manifold , type (biology) , pure mathematics , geometry , scalar curvature , computer science , curvature , artificial intelligence , sectional curvature , mechanical engineering , ecology , biochemistry , chemistry , repressor , biology , transcription factor , engineering , gene
Let ( M , g ) be a compact oriented Riemannian manifold with an incomplete edge singularity. This article shows that it is possible to evolve g by the Yamabe flow within a class of singular edge metrics. As the main analytic step we establish parabolic Schauder‐type estimates for the heat operator on certain Hölder spaces adapted to the singular edge geometry. We apply these estimates to obtain local existence for a variety of quasilinear equations, including the Yamabe flow. This provides a setup for a subsequent discussion of the Yamabe problem using flow techniques in the singular setting.