Author

Xin-Xiu Zhang

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Preprint Oct 2026

Curvature measures and volume preserving flows in h-convex geometry

In this paper, we introduce a concept of modified curvature measures for h-convex domains in hyperbolic space and prove a shifted version of the generalized Alexandrov theorem, which characterizes geodesic balls in hyperbolic space via modified curvature measures. This result generalizes the classical work of Kohlmann...

Xin-Xiu Zhang · 1 citation

Preprint Oct 2026

Modified support measures and Alexandrov-Fenchel type inequalities for nonsmooth h-convex bodies in hyperbolic space

We establish the Alexandrov-Fenchel inequality and its modified version for arbitrary, possibly nonsmooth, horospherically convex bodies in hyperbolic space $\mathbb{H}^{n+1}, n\geq 2$, and prove that equality in each inequality holds if and only if the h-convex body is a geodesic ball. A key ingredient is a rigidity t...

Xin-Xiu Zhang · 0 citations