Exact Discretization of Harmonic Tensors
| Autor: | Timothy Chumley, Renato Feres, Matthew Wallace |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Discretization 010102 general mathematics Connection (vector bundle) Mathematical analysis Holonomy Harmonic (mathematics) Orthonormal frame 01 natural sciences Potential theory Tensor field 010104 statistics & probability Differential Geometry (math.DG) Harmonic function FOS: Mathematics 0101 mathematics Analysis Mathematics |
| Zdroj: | Potential Analysis. 56:409-421 |
| ISSN: | 1572-929X 0926-2601 |
| DOI: | 10.1007/s11118-020-09889-7 |
| Popis: | Lyons and Sullivan have shown how to discretize harmonic functions on a Riemannian manifold $M$ whose Brownian motion satisfies a certain recurrence property called $\ast$-recurrence. We study analogues of this discretization for tensor fields which are harmonic in the sense of the covariant Laplacian. We show that, under certain restrictions on the holonomy of the connection, the lifted diffusion on the orthonormal frame bundle has the same $\ast$-recurrence property as the original Brownian motion. This observation permits us to reduce to the discretization of ordinary harmonic functions by a device called scalarization. Comment: 15 pages |
| Databáze: | OpenAIRE |
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