https://neckpinch.com/authors/mohammad-n-ivaki/New arXiv papers by Mohammad N. Ivaki, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2408.06057arxiv:2408.06057Mon, 12 Aug 2024 00:00:00 GMTYingxiang Hu, Mohammad N. Ivaki — In the first part of this paper, we study the following non-homogeneous, locally constrained inverse curvature flow in Euclidean space ℝⁿ⁺¹, \beginalign* \dotx=\left(\frac1{\frac{E_k(\hatκ)}{E_k-1(\hatκ)}-α}-\langle x,ν\rangle\right)ν, \quad k=2,3,\ldots,n-1. \endalign* Assuming that the initial hypersurface 𝓜₀ ⊂ ℝⁿ⁺¹ is star-shaped and its shifted principal curvatures hatκ=κ+α(1,…,1) lie in the convex set \beginalign* Γ_α,k:=Γ_k-1\cap \{λ\in \mathbbR^n:\, E_k(λ)-αE_k-1(λ)>0\}, \endalign* we show that the flow admits a smooth solution that exists for all positive times, and it converges smoothly to a round sphere. As a corollary, we obtain a new set of Alexandrov-Fenchel-type inequalities for non-convex domains. In the second part, we derive a Poincaré type inequality for k-convex hypersurfaces which complements a more general version of the well-known Heintze-Karcher inequality.Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsHomogeneous spacesLong-time existence & convergenceGeometric inequalities https://arxiv.org/abs/2304.12839arxiv:2304.12839Tue, 25 Apr 2023 00:00:00 GMTMohammad N. Ivaki, Emanuel Milman — Employing a local version of the Brunn-Minkowski inequality, we give a new and simple proof of a result due to Andrews, Choi and Daskalopoulos that the origin-centred balls are the only closed, self-similar solutions of the Gauss curvature flow. Extensions to various non-linearities are obtained, assuming the centroid of the enclosed convex body is at the origin. By applying our method to the Alexandrov-Fenchel inequality, we also show that origin-centred balls are the only solutions to a large class of even Christoffel-Minkowski type problems.Other curvature flowsGauss curvature flowStability & uniquenessGeometric inequalities