2025/11/02 by Karsten Bohlen, Bohlen, Karsten
Mathematics · #35K67 #47J35 #58H05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2511.00991
openalex publication_date 2025/11/02 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
A pseudodifferential Volterra calculus for inverting parabolic differential equations on Lie groupoids is introduced. This enables the study of fundamental solutions of various cases of heat flows on singular manifolds with corners with non-resonant boundary indicial symbols, such as the b-manifolds, as well as other geometric bisection covariant heat flows. We also establish the short time asymptotic expansion for the heat kernel of a positive, elliptic differential operator on a Lie groupoid that acts on suitable Sobolev Hilbert modules and is positive definite with respect to the appropriate L2 inner product.