Covariant Schrödinger semigroups on Riemannian manifolds

2018/01/04 by Batu Güneysu, Güneysu, Batu · 1 citation
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR) #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1801.01335

openalex publication_date 2018/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

This monograph develops the theory of covariant Schrödinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. Basis differential operators in Riemannian manifolds IV. Some specific results for the minimal heat kernel V. Wiener measure and Brownian motion on Riemannian manifolds VI. Contractive Dynkin and Kato potentials VII. Foundations of covariant Schrödinger semigroups VIII. Compactness of V(H^∇+1)^-1 IX. L^q-properties of covariant Schrödinger semigroups X. Continuity properties of covariant Schrödinger semigroups XI. Integral kernels for covariant Schrödinger semigroups XII. Essential self-adjointness of covariant Schrödinger semigroups XIII. Smooth compactly supported sections as form core XIV. Applications (in quantum mechanics and geometric analysis)

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• L^p-Boundedness of the Covariant Riesz Transform on Differential Forms for p>2

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