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arXiv · 2403.07281

Locally constrained flows and geometric inequalities in sphere

Shanwei Ding·Guanghan Li
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Abstract

In this paper, we uncover an intriguing algebra property of an element symmetric polynomial. By this property, we establish the longtime existence and convergence of a locally constrained flow, thereby some families of geometric inequalities in sphere can be derived. Meanwhile, a new family of ``three terms'' geometric inequalities involving two weighted curvature integrals and one quermassintegral are proved. Unlike hyperbolic spaces, we also obtain an inverse weighted geometric inequality in sphere.

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Shanwei Ding, Guanghan Li. 2024-03-12. Locally constrained flows and geometric inequalities in sphere. https://arxiv.org/abs/2403.07281

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