A comparison theorem with applications to sharp geometric inequalities for submanifolds

2026/05/07 by Shengliang Pan, Chengyang Yi
#math.DG

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Abstract

In this paper, we derive an explicit expression for the Jacobian determinant of the normal exponential map on a submanifold, establishing a relationship with its ambient counterpart. This formula leads to a new comparison theorem which is closely related to the comparison theorem of Heintze-Karcher. As applications, we obtain a Fenchel-Borsuk-Chern-Lashof-type inequality and a Willmore-Chen-type inequality on closed submanifolds in complete noncompact manifolds with nonnegative curvature and Euclidean volume growth.

Citations

• Geometric inequalities and the Alexandrov-Bakelman-Pucci technique

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