Levy Laplacian on manifold and heat flows of differential forms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918095860269056 |
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| author | Volkov, Boris |
| author_facet | Volkov, Boris |
| contents | The Levy Laplacian is an infinite-dimensional differential operator, which is interesting for its connection with the Yang-Mills gauge fields. The article proves the equivalence of various definitions of the Levy Laplacian on the manifold of $H^1$-paths on a Riemannian manifold. The heat equation with the Levy Laplacian is considered. The tendency of some solutions of this heat equation to the locally constant functionals as time tends to infinity is studied. These solutions are constructed using heat flows of differential forms on the compact Riemannian manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Levy Laplacian on manifold and heat flows of differential forms Volkov, Boris Mathematical Physics Differential Geometry Functional Analysis 70S15, 58B20, 58J35, 53C07 The Levy Laplacian is an infinite-dimensional differential operator, which is interesting for its connection with the Yang-Mills gauge fields. The article proves the equivalence of various definitions of the Levy Laplacian on the manifold of $H^1$-paths on a Riemannian manifold. The heat equation with the Levy Laplacian is considered. The tendency of some solutions of this heat equation to the locally constant functionals as time tends to infinity is studied. These solutions are constructed using heat flows of differential forms on the compact Riemannian manifold. |
| title | Levy Laplacian on manifold and heat flows of differential forms |
| topic | Mathematical Physics Differential Geometry Functional Analysis 70S15, 58B20, 58J35, 53C07 |
| url | https://arxiv.org/abs/2507.13013 |