Extinction profile of complete non-compact solutions to the Yamabe flow

Panagiota Daskalopoulos, John King, Natasa Sesum

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

This work addresses the singularity formation of complete non-compact solutions to the conformally flat Yamabe flow whose conformal factors have cylindrical behavior at infinity. Their singularity profiles happen to be Yamabe solitons, which are self-similar solutions to the fast diffusion equation satisfied by the conformal factor of the evolving metric. The self-similar profile is determined by the second order asymptotics at infinity of the initial data which is matched with that of the corresponding self-similar solution. Solutions may become extinct at the extinction time T of the cylindrical tail or may live longer than T. In the first case the singularity profile is described by a Yamabe shrinker that becomes extinct at time T. In the second case, the singularity profile is described by a singular Yamabe shrinker slightly before T and by a matching Yamabe expander slightly after T .

Original languageEnglish (US)
Pages (from-to)1757-1798
Number of pages42
JournalCommunications in Analysis and Geometry
Volume27
Issue number8
DOIs
StatePublished - 2019

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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