## 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 ⊂ ℂ^{n} ×^{m} . As a consequence, we can also compute the heat kernel associated with the weighted ∂̄ -equation in ℂ^{n} when the weight is given by exp(-φ(z,z) λ) where φ:ℂ^{n} ×ℂ ^{n} →ℂ^{m} is a quadratic, sesquilinear form and λ ∈ ℝ^{m} . Our method involves the representation theory of the Lie group M and the group Fourier transform.

Original language | English (US) |
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Pages (from-to) | 256-275 |

Number of pages | 20 |

Journal | Journal of Geometric Analysis |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2011 |

Externally published | Yes |

## 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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