The Li-Yau-Hamilton Estimate and the Yang-Mills Heat Equation on Manifolds with Boundary

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dc.creatorPulemotov, Artem
dc.date2008-03-07
dc.date2008-09-18
dc.date.accessioned2026-07-07T10:18:08Z
dc.date.available2026-07-07T10:18:08Z
dc.descriptionThe paper pursues two connected goals. Firstly, we establish the Li-Yau-Hamilton estimate for the heat equation on a manifold $M$ with nonempty boundary. Results of this kind are typically used to prove monotonicity formulas related to geometric flows. Secondly, we establish bounds for a solution $\nabla(t)$ of the Yang-Mills heat equation in a vector bundle over $M$. The Li-Yau-Hamilton estimate is utilized in the proofs. Our results imply that the curvature of $\nabla(t)$ does not blow up if the dimension of $M$ is less than 4 or if the initial energy of $\nabla(t)$ is sufficiently small.
dc.description37 pages
dc.identifierhttps://arxiv.org/abs/0803.1015
dc.identifierhttp://arxiv.org/abs/0803.1015
dc.identifierJournal of Functional Analysis 255 (2008), pages 2933-2965
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174093
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.titleThe Li-Yau-Hamilton Estimate and the Yang-Mills Heat Equation on Manifolds with Boundary
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