59 citations · 268 across the 39 of their papers we have counts for
45 papers
Centro-affine spectral geometry of polytopes
Yingxiang Hu, Mohammad N. Ivaki
In this paper, we develop a polyhedral version of Milman's centro-affine spectral framework for full-dimensional origin-symmetric polytopes. A weighted graph Laplacian on the facet…
Weighted centro-affine Poincaré inequalities
Yingxiang Hu, Mohammad N. Ivaki
We obtain weighted centro-affine Bochner formulas on spherical caps associated with smooth strictly convex hypersurfaces. As a consequence, we prove weighted Poincaré inequalities…
Centro-affine Poincaré inequality: Unconditional convex bodies
Yingxiang Hu, Mohammad N. Ivaki
We prove that the centro-affine Poincaré inequality holds with constant for every unconditional convex body and every smooth function with natural orthogonality…
Capillary -curvature problem
Yingxiang Hu, Mohammad N. Ivaki
We prove a gradient estimate for a class of capillary curvature equations in the half-space. As an application, we prove the existence of an even, smooth, strictly convex solution…
Capillary -Christoffel-Minkowski problem
Yingxiang Hu, Mohammad N. Ivaki
We solve the capillary -Christoffel--Minkowski problem in the half-space for in the class of even hypersurfaces. A crucial ingredient is a non-collapsing estimate th…
On the conjectured capillary Blaschke-Santaló inequality
Carlos Cabezas-Moreno, Yingxiang Hu, Mohammad N. Ivaki
We prove that the conjectured capillary Blaschke--Santaló inequality holds for any unconditional, strictly convex capillary hypersurface when . Mor…
Capillary curvature images
Yingxiang Hu, Mohammad N. Ivaki
In this paper, we solve the even capillary -Minkowski problem for the range and . Our approach is based on an iterative scheme that builds on…
Capillary Christoffel-Minkowski problem
Yingxiang Hu, Mohammad N. Ivaki, Julian Scheuer
The result of Guan and Ma (Invent. Math. 151 (2003)) states that if is spherically convex, then arises as the curvature (the -…
New quermassintegral and Poincaré type inequalities for non-convex domains
Yingxiang 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 , \begin{align*} \dot{x}=\l…
Stability of the cone-volume measure with near constant density
Yingxiang Hu, Mohammad N. Ivaki
We prove that if the density of the cone-volume measure of a smooth, strictly convex body with respect to the spherical Lebesgue measure is nearly constant, then a homothetic copy…
Prescribed curvature problem
Yingxiang Hu, Mohammad N. Ivaki
In this paper, we establish the existence of smooth, origin-symmetric, strictly convex solutions to the prescribed even curvature problem.
On the uniqueness of solutions to the isotropic dual Minkowski problem
Yingxiang Hu, Mohammad N. Ivaki
We prove that the unit sphere is the only smooth, strictly convex solution to the isotropic dual Minkowski problem \begin{align*} h^{p-1} |D h|^{n+1-q}\mathcal{K}=1, \end{ali…
Uniqueness of solutions to a class of non-homogeneous curvature problems
Mohammad N. Ivaki
We show that the only even, smooth, convex solutions to a class of isotropic mixed Christoffel-Minkowski type problems are origin-centred spheres, which, in particular, answers a q…
-Minkowski Problem under Curvature Pinching
Mohammad N. Ivaki, Emanuel Milman
Let be a smooth, origin-symmetric, strictly convex body in . If for some , the anisotropic Riemannian metric $\frac{1}{2}D^2 \Vert\cdot\…
Uniqueness of solutions to a class of isotropic curvature problems
Mohammad 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…
On the stability of the -curvature
Mohammad N. Ivaki
It is known that the -curvature of a smooth, strictly convex body in is constant only for origin-centred balls when , and only for balls when $p=1…
Constant rank theorems for curvature problems via a viscosity approach
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
An important set of theorems in geometric analysis consists of constant rank theorems for a wide variety of curvature problems. In this paper, for geometric curvature problems in c…
Christoffel-Minkowski flows
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
We provide a curvature flow approach to the regular Christoffel-Minkowski problem. The speed of our curvature flow is of an entropy preserving type and contains a global term.
Parabolic approaches to curvature equations
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
We employ curvature flows without global terms to seek strictly convex, spacelike solutions of a broad class of elliptic prescribed curvature equations in the simply connected Riem…
Mean convex mean curvature flow with free boundary
Nick Edelen, Robert Haslhofer, Mohammad N. Ivaki +1
In this paper, we generalize White's regularity and structure theory for mean-convex mean curvature flow to the setting with free boundary. A major new challenge in the free bounda…
Iterations of curvature images
Mohammad N. Ivaki
We study the iterations of a class of curvature image operators introduced by the author in (J. Funct. Anal. 271 (2016) 2133--2165). The fixed points of these operators are…
Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings In Minkowski Space And The Cross Curvature Flow
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
This short note is a mostly expository article examining negatively curved three-manifolds. We look at some rigidity properties related to isometric embeddings into Minkowski space…
Deforming a hypersurface by principal radii of curvature and support function
Mohammad N. Ivaki
We study the motion of smooth, closed, strictly convex hypersurfaces in expanding in the direction of their normal vector field with speed depending on the th…
Low complexity solutions of the Allen-Cahn equation on three-spheres
Robert Haslhofer, Mohammad N. Ivaki
In this short note, we prove that on the three-sphere with any bumpy metric there exist at least four solutions of the Allen-Cahn equation with spherical interface and index at mos…