Add to ORKGWe provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body Ω. The bound depends only on the perimeter and inradius r of the original body and states that |∂Ω_t| ≥ (1−t/r)^(n−1)₊|∂Ω|. In particular the bound is independent of any regularity properties of ∂Ω. As a by-product of the proof we establish precise conditions for equality. The proof, which is straightforward, is based on the construction of an extremal set for a certain optimization problem and the use of basic properties of mixed volumes
We consider surfaces which minimize a nonlocal perimeter functional and we discuss their interior re...
The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane an...
AbstractLutwak, Yang and Zhang defined the cone volume functional U over convex polytopes in Rn cont...
In this note we introduce a pseudometric on convex planar curves based on distances between normal l...
In this note we introduce a pseudometric on convex planar curves based on distances between normal l...
We show that the maximum total perimeter ofk plane convex bodies with disjoint interiors lying insid...
Let $E\subset \mathbb R^n$, $n\ge 2$, be a set of finite perimeter with $|E|=|B|$, where $B$ denotes...
We prove a lower bound on the number of the convex components of a compact set with non-empty interi...
Abstract. Steiner symmetrization along n linearly independent directions transforms every compact su...
We solve several new sharp inequalities relating three quantities amongst the area, perimeter, inrad...
Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \l...
Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \l...
Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \l...
For two planar convex bodies, C and D, consider a packing S of n positive homothets of C contained i...
We provide a sharp double-sided estimate for Poincaré–Sobolev constants on a convex set, in terms of...
We consider surfaces which minimize a nonlocal perimeter functional and we discuss their interior re...
The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane an...
AbstractLutwak, Yang and Zhang defined the cone volume functional U over convex polytopes in Rn cont...
In this note we introduce a pseudometric on convex planar curves based on distances between normal l...
In this note we introduce a pseudometric on convex planar curves based on distances between normal l...
We show that the maximum total perimeter ofk plane convex bodies with disjoint interiors lying insid...
Let $E\subset \mathbb R^n$, $n\ge 2$, be a set of finite perimeter with $|E|=|B|$, where $B$ denotes...
We prove a lower bound on the number of the convex components of a compact set with non-empty interi...
Abstract. Steiner symmetrization along n linearly independent directions transforms every compact su...
We solve several new sharp inequalities relating three quantities amongst the area, perimeter, inrad...
Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \l...
Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \l...
Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \l...
For two planar convex bodies, C and D, consider a packing S of n positive homothets of C contained i...
We provide a sharp double-sided estimate for Poincaré–Sobolev constants on a convex set, in terms of...
We consider surfaces which minimize a nonlocal perimeter functional and we discuss their interior re...
The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane an...
AbstractLutwak, Yang and Zhang defined the cone volume functional U over convex polytopes in Rn cont...