Philipp Schange

collaborators

4 papers

math.PR2026

Angles and volumes of simplices, boxes, and crosspolytopes in constant curvature

Zakhar Kabluchko, Philipp Schange

We determine, up to isometry, the Riemannian tangent and normal cones at arbitrary faces of boxes, acute orthocentric simplices, rectangular simplices, and asymmetric crosspolytope…

math.PR2026

Expected hyperbolic volumes of random beta polytopes

Zakhar Kabluchko, Philipp Schange

Let $X_{1}, \dots, X_{n}$ be independent random points in the closed unit ball of $R^{d}$ . Assume that each $X_{i}$ has a beta distribution with parameter $β_{i} \geq - 1$ : if $β_{i} > - 1$ …

math.MG2025

Volumes of Regular Hyperbolic Simplices

Zakhar Kabluchko, Philipp Schange

We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.

math.MG2025

Angles of orthocentric simplices

Zakhar Kabluchko, Philipp Schange

A $d$ -dimensional simplex in Euclidean space is called orthocentric if all of its altitudes intersect at a single point, referred to as the orthocenter. We explicitly compute the i…