In this survey article we will consider universal lower bounds on the volume of a Riemannian
manifold, given in terms of the volume of lower dimensional objects (primarily the lengths of …

Abstract Aspect-Oriented Programming (AOP) promises separation of concerns at the
implementation level. However, aspects are not always orthogonal and aspect interaction is …

We say that a Riemannian manifold (M, g) with a non-empty boundary∂ M is a minimal
orientable filling if, for every compact orientable (M̃, g̃) with∂ M̃=∂ M, the inequality d g̃ (x …

In this paper we consider metric fillings of boundaries of convex bodies. We show that
convex bodies are the unique minimal fillings of their boundary metrics among all integral …

We study metric spaces homeomorphic to a closed oriented manifold from both geometric
and analytic perspectives. We show that such spaces (which are sometimes called metric …

The main" unconditional" result of this paper, Theorem 3, states that every two-dimensional
affine disc in a normed space (that is, a disc contai in a two-dimensional affine subspace) is …

We study the differentiability of the stable norm"." associated with a Zn periodic metric on Rn.
Extending one of the main results of [Ba2], we prove that if p∈ Rn and the coordinates of p …

Methods of estimating (Riemannian and Finsler) filling volumes by using nonexpanding
maps to Banach spaces of $ L^\infty $-type are developed and generalized. For every …

We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the
conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0. We …

This paper is a continuation of our paper about boundary rigidity and filling minimality of
metrics close to flat ones. We show that compact regions close to a hyperbolic one are …