A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
Microlocal analysis for differential operators , series =
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Defines a Dirichlet-to-Neumann map for the spectral fractional Laplacian with inhomogeneous data, analyzes the inverse problem of recovering information from it, and proves a density result.
The first correction term in the mean first capture time of shrinking geodesic balls by isotropic Lévy flights on Zoll surfaces is determined by the degree of the conjugate point.
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Inverse problems for the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data
Defines a Dirichlet-to-Neumann map for the spectral fractional Laplacian with inhomogeneous data, analyzes the inverse problem of recovering information from it, and proves a density result.