arXiv subjects

Carlos Cabezas-Moreno

Publications and source records attributed to Carlos Cabezas-Moreno.

3 recordsLinked to original sources

arXiv2026

On a question by Firey concerning uniqueness

We prove that the curvature equation $\sum_{j=1}^n α_j E_j(τ_{\mathcal{M}})=\sum_{j=1}^n α_j E_j(τ_{\mathcal{N}})$ yields uniqueness up to translation for any two closed $C^2_+$ hypersurfaces $\mathcal{M}, \mathcal{N}\hookrightarrow\mathbb{R}^{n+1}$ whenever $(α_1,\ldots,α_n)\in\mathbb{R}_{\geq 0}^n\setminus\{0\}$ is log-concave and has no internal zeros. This gives an affirmative answer to a uniqueness question posed by Firey in the $C^2_+$ class.

math.DG↗

arXiv2026

On the conjectured capillary Blaschke-Santaló inequality

We prove that the conjectured capillary Blaschke--Santaló inequality holds for any unconditional, strictly convex capillary hypersurface when $θ\in \left(0, \tfracπ{2}\right)$. Moreover, for $θ\in \left(\tfracπ{2}, π\right)$, we show that the capillary volume product has no finite upper bound.

math.DG↗

arXiv2025

The $L_{p}$ dual Christoffel-Minkowski problem for $1<p<q\leq k+1$ with $1\leq k\leq n$

In this paper, we investigate an $L_{p}$ Christoffel-Minkowski-type problem that prescribes a class of $L_p$ geometric measures, which are mixtures of the $k$-th area measure and the $q$-th dual curvature measure. By establishing a gradient estimate, we obtain the existence of an even, smooth, strictly convex solution to this problem for $1 < p < q \leq k + 1$, where $1 \leq k \leq n$ and $n \geq 1$.

math.AP↗