42 citations · 159 across the 17 of their papers we have counts for
17 papers
A sharp lower bound on the mean curvature integral with critical power for integral varifolds
Ulrich Menne
Part I Weakly differentiable functions Part II PDEs on varifolds 15 Sobolev spaces ... 75 16 Preliminaries ... 82 17 Maximum estimates ... 86 18 Second order flatness of Lebesgue s…
A priori bounds for geodesic diameter. Part II. Fine connectedness properties of varifolds
Ulrich Menne, Christian Scharrer
For varifolds whose first variation is representable by integration, we introduce the notion of indecomposability with respect to locally Lipschitzian real valued functions. Unlike…
A priori bounds for geodesic diameter. Part I. Integral chains with coefficients in a complete normed commutative group
Ulrich Menne, Christian Scharrer
As service to the community, we provide - for Euclidean space - a basic treatment of locally rectifiable chains and of the complex of locally integral chains. In this setting, we m…
Pointwise differentiability of higher order for distributions
Ulrich Menne
For distributions, we build a theory of higher order pointwise differentiability comprising, for order zero, Łojasiewicz's notion of point value. Results include Borel regularity o…
A priori bounds for geodesic diameter. Part III. A Sobolev-Poincaré inequality and applications to a variety of geometric variational problems
Ulrich Menne, Christian Scharrer
Based on a novel type of Sobolev-Poincaré inequality (for generalised weakly differentiable functions on varifolds), we establish a finite upper bound of the geodesic diameter of g…
The concept of varifold
Ulrich Menne
We survey - by means of 20 examples - the concept of varifold, as generalised submanifold, with emphasis on regularity of integral varifolds with mean curvature, while keeping prer…
A geometric second-order-rectifiable stratification for closed subsets of Euclidean space
Ulrich Menne, Mario Santilli
Defining the -th stratum of a closed subset of an dimensional Euclidean space to consist of those points, where it can be touched by a ball from at least linearly inde…
An isoperimetric inequality for diffused surfaces
Ulrich Menne, Christian Scharrer
For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev ty…
Pointwise differentiability of higher order for sets
Ulrich Menne
The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to tho…
Sobolev functions on varifolds
Ulrich Menne
This paper introduces first order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally nonlinear class of generalise…
Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds
Sławomir Kolasiński, Ulrich Menne
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study…
Weakly differentiable functions on varifolds
Ulrich Menne
The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept propo…
Optimal Degree of Optical Circuit Switching in IP-over-WDM Networks
Ulrich Menne, Christian Raack, Roland Wessaly +1
In this paper, we study the influence of technology, traffic properties and price trends on optimized design of a reference IP-over-WDM network with rich underlying fiber topology.…
Decay estimates for the quadratic tilt-excess of integral varifolds
Ulrich Menne
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Le…
Some Applications of the Isoperimetric Inequality for Integral Varifolds
Ulrich Menne
In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Cal…
Second order rectifiability of integral varifolds of locally bounded first variation
Ulrich Menne
In this work it is shown that every integral varifold in an open subset of Euclidian space of locally bounded first variation can be covered by a countable collection of submanifol…
A Sobolev Poincaré type inequality for integral varifolds
Ulrich Menne
In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained…