Backward propagation of warped product structures and asymptotically conical shrinkers

Brett Kotschwar

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arXiv · 2401.00606

Backward propagation of warped product structures and asymptotically conical shrinkers

Brett Kotschwar

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Abstract

We establish sufficient conditions which ensure that a locally-warped product structure propagates backward in time under the Ricci flow. As an application, we prove that if an asymptotically conical gradient shrinking soliton is asymptotic to a cone whose cross-section is a product of Einstein manifolds, the soliton must itself be a multiply-warped product over the same manifolds.

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BibTeX RIS

Brett Kotschwar. 2023-12-31. Backward propagation of warped product structures and asymptotically conical shrinkers. https://arxiv.org/abs/2401.00606

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