The □b-heat equation on quadric manifolds

Albert Boggess, Andrew Raich

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

In this article, we give an explicit calculation of the partial Fourier transform of the fundamental solution to the □b -heat equation on quadric submanifolds M ⊂ ℂn ×m . As a consequence, we can also compute the heat kernel associated with the weighted ∂̄ -equation in ℂn when the weight is given by exp(-φ(z,z) λ) where φ:ℂn ×ℂ n →ℂm is a quadratic, sesquilinear form and λ ∈ ℝm . Our method involves the representation theory of the Lie group M and the group Fourier transform.

Original languageEnglish (US)
Pages (from-to)256-275
Number of pages20
JournalJournal of Geometric Analysis
Volume21
Issue number2
DOIs
StatePublished - Apr 1 2011
Externally publishedYes

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Keywords

  • Fundamental solution
  • Heat equation
  • Heat kernel
  • Heisenberg group
  • Kohn Laplacian
  • Lie group
  • Quadric manifold

ASJC Scopus subject areas

  • Geometry and Topology

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