arXiv subjects

Caroline VanBlargan

Publications and source records attributed to Caroline VanBlargan.

3 recordsLinked to original sources

arXiv2022

Stability of quermassintegral inequalities along inverse curvature flows

In this paper, we consider the stability of quermassintegral inequalities along a inverse curvature flow. We choose a special rescaling of the flow such that the $k$-th quermassintegral is decreasing and the $k-1$-th quermassintegral is preserved. Along this rescaled flow, we prove that the decreasing rate of the $k$-th quermassintegral is faster than the Fraenkel asymmetry of the domain when approaching to the sphere. This leads to the stability inequality of quermassintegral inequalities for nearly spherical sets using the flow method.

math.DG↗

arXiv2022

Quantitative Quermassintegral Inequalities for Nearly Spherical Sets

In this paper, we establish quantitative Alexandrov-Fenchel inequalities for quermassintegrals on nearly spherical sets. In particular, we bound the $(k,m)$-isoperimetric deficit from below by the Frankael asymmetry. We also find a lower bound on the $(k,m)$-isoperimetric deficit using the spherical deviation.

math.DG↗

arXiv2014

Equitable Mirrors

In this article we explore some finer properties of equi-areal mirrors and introduce techniques for developing new mirror surfaces that simultaneously minimize angular and areal distortion.

astro-ph.IM↗