Kac regular sets and Sobolev spaces in geometry, probability and quantum physics

DOI10.1007/s00208-019-01932-2zbMath1461.81047arXiv1708.05542OpenAlexW2999461301WikidataQ126320193 ScholiaQ126320193MaRDI QIDQ2664164

Batu Güneysu, Francesco Bei

Publication date: 20 April 2021

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05542

zbMATH Keywords

first penetration timeKato decomposable potential : Riemannian spin manifoldopen subset \(\Omega\)

Mathematics Subject Classification ID

Brownian motion (60J65) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Spinor and twistor methods applied to problems in quantum theory (81R25) Quantum stochastic calculus (81S25) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Boundary value problems for linear higher-order PDEs (35G15) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Related Items (2)

Kac regularity and domination of quadratic forms ⋮ Symmetry of solutions to semilinear PDEs on Riemannian domains

Cites Work

• On generalized Schrödinger semigroups
• Dirichlet parabolicity and \(\mathsf{L}^{1}\)-Liouville property under localized geometric conditions
• A canonical decomposition for quadratic forms with applications to monotone convergence theorems
• Dirichlet forms and symmetric Markov processes
• Covariant Schrödinger semigroups on Riemannian manifolds
• Perturbation of Dirichlet forms by measures
• Nonrelativistic hydrogen type stability problems on nonparabolic 3-manifolds
• L^1-elliptic regularity and H = W on the whole L^p-scale on arbitrary manifolds
• Heat equation derivative formulas for vector bundles
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