Small time heat expansion of the laplacian on an analytic hypersurface with an isolated singularity

2022/07/13 by Demetrios A. Pliakis, Pliakis, Demetrios A.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2207.06164

openalex publication_date 2022/07/13 · openalex created_date 2022/07/15 · openalex updated_date 2026/07/28

Abstract

I prove the existence of small time heat expansion for the Laplace operator on an analytic hypersurface with an isolated singularity. First we obtain a local parametrization of the hypersurface near the singularity. We introduce the notion of quasihomogeneous tangent cone. Then perturb the parametrization of the cone employing a Newton scheme and obtain a parametrization with functions of specific form. These allow us to obtain local models for the Laplace operator near the singularity. These are operators with irregular singularities. We derive the estimates required by singular asymptotics.

Related

• Heat trace expansion on manifolds with conic singularities
• Heat trace asymptotics for wedge-like singularity
• Local Geometry of Singular Real Analytic Surfaces
• Spectral Functions of Singular Operators
• The spectrum of the Laplacian on closed manifolds and the heat asymptotics near conical points