Bismut hypoelliptic Laplacians for manifolds with boundaries

Francis Nier; Shu Shen

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arXiv · 2107.01958

Bismut hypoelliptic Laplacians for manifolds with boundaries

Francis Nier·Shu Shen

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Abstract

Boundary conditions for Bismut's hypoelliptic Laplacian which naturally correspond to Dirichlet and Neumann boundary conditions for Hodge Laplacians are considered. Those are related with specific boundary conditions for the differential and its various adjoints. Once the closed realizations of those operators are well understood, the commutation of the differential with the resolvent of the hypoelliptic Laplacian is checked with other properties like the PT-symmetry, which are important for the spectral analysis.

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Francis Nier, Shu Shen. 2021-07-05. Bismut hypoelliptic Laplacians for manifolds with boundaries. https://arxiv.org/abs/2107.01958

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