The Li-Yau-Hamilton estimate and the Yang-Mills heat equation on manifolds with boundary |
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Authors: | Artem Pulemotov |
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Institution: | Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853-4201, USA |
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Abstract: | The 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 ∇(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 ∇(t) does not blow up if the dimension of M is less than 4 or if the initial energy of ∇(t) is sufficiently small. |
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Keywords: | Heat equation Harnack inequality Yang-Mills Reflecting Brownian motion |
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