Isometric embeddings via heat kernel

Xiaowei Wang, Ke Zhu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

For any n-dimensional compact Riemannian manifold M with smooth metric g, we construct a canonical t-family of isometric embeddings It : M → ℝq(t), with t > 0 sufficiently small and q (t ) 蠑 t-n/2. This is done by intrinsically perturbing the heat kernel embedding introduced in [BBG]. As t → 0+, asymptotic geometry of the embedded images is discussed.

Original languageAmerican English
Pages (from-to)497-538
Number of pages42
JournalJournal of Differential Geometry
Volume99
Issue number3
DOIs
StatePublished - Mar 1 2015

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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