The □b-heat equation on quadric manifolds

Albert Boggess, Andrew Raich

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 2011
Externally publishedYes

Fingerprint

Quadric
Heat Equation
Fourier transform
Sesquilinear form
Heat Kernel
Fundamental Solution
Representation Theory
Submanifolds
Partial

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

The □b-heat equation on quadric manifolds. / Boggess, Albert; Raich, Andrew.

In: Journal of Geometric Analysis, Vol. 21, No. 2, 04.2011, p. 256-275.

Research output: Contribution to journalArticle

Boggess, Albert ; Raich, Andrew. / The □b-heat equation on quadric manifolds. In: Journal of Geometric Analysis. 2011 ; Vol. 21, No. 2. pp. 256-275.
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