Related papers: A hyperplane inequality for the surface area of pr…

We prove several stability and volume difference inequalities for projections of convex bodies and apply them to prove a hyperplane inequality for surface area of projection bodies.

We provide general inequalities that compare the surface area S(K) of a convex body K in ${\mathbb R}^n$ to the minimal, average or maximal surface area of its hyperplane or lower dimensional projections. We discuss the same questions for…

We prove an inequality that extends to arbitrary measures the hyperplane inequality for volume of unconditional convex bodies originally observed by Bourgain.

We prove a counterpart of the log-convex density conjecture in the hyperbolic plane.

In this paper, the mixed Lp-surface area measures are defined and the mixed Lp Minkowski inequality is obtained consequently. Furthermore, the mixed Lp projection inequality for mixed projection bodies is established.

In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.

Using gnomonic projection and Poincar\'e model, we first define the spherical projection body and hyperbolic projection body in spherical space $\mathbb{S}^n$ and hyperbolic space $\mathbb{H}^n$, then define the spherical Steiner…

We prove an estimate for arbitrary measure of sections of convex bodies. The proof is based on a stability result for intersection bodies.

In this article, we prove a geometric inequality for star-shaped and mean-convex hypersurfaces in hyperbolic space by inverse mean curvature flow. This inequality can be considered as a generalization of Willmore inequality for closed…

We determine non-Hopf hypersurfaces with constant mean curvature in the complex projective plane which attain equality in a basic inequality between the maximum Ricci curvature and the squared mean curvature.

Let X be a smooth cubic hypersurface. We prove that a general cubic surface is isomorphic to a hyperplane section of X .

In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we…

We give a short and simple proof of Cauchy's surface area formula, which states that the average area of a projection of a convex body is equal to its surface area up to a multiplicative constant in the dimension.

We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.

A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.

We show that the hyperplane conjecture holds for the classes of $k$-intersection bodies with arbitrary measures in place of volume.

We present an algebro-geometric proof of the K-semistability of the projective plane.

An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.

We will formulate and prove a generalization of the isoperimetric inequality in the plane. Using this inequality we will construct an unitary space - and in consequence - an isomorphic copy of a separable infinite dimensional Hilbert space,…

In this paper, we prove a family of sharp geometric inequalities for free boundary hypersurfaces in a ball in space forms.