Deyan Zhang | Searcharxiv

arXiv2024

Deforming Locally Convex Curves into Curves of Constant $k$-order Width

A nonlocal curvature flow is introduced to evolve locally convex curves in the plane. It is proved that this flow with any initial locally convex curve has a global solution, keeping the local convexity and the elastic energy of the evolving curve, and that, as the time goes to infinity, the curve converges to a smooth, locally convex curve of constant $k$-order width. In particular, the limiting curve is a multiple circle if and only if the initial locally convex curve is $k$-symmetric.

math.DG↗

arXiv2018

The log-Brunn-Minkowski inequality in $\mathbb{R}^3$

Böröczky, Lutwak, Yang and Zhang recently proved the log-Brunn-Minkowski inequality which is stronger than the classical Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane. This paper establishes the log-Brunn-Minkowski, log-Minkowski, $L_p$-Minkowski and $L_p$-Brunn-Minkowski inequalities for two convex bodies in $\mathbb{R}^3$.

math.DG↗