183 citations · 612 across the 21 of their papers we have counts for
21 papers
Measure-valued valuations on star bodies
Jorge S. Ibáñez-Marcos, Monika Ludwig, Pedro Tradacete +1
A complete classification of weak~continuous, measure-valued valuations is established on star bodies in . Consequences are an integral representation of rotation equivar…
Unimodular Valuations beyond Ehrhart
Ansgar Freyer, Monika Ludwig, Martin Rubey
A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. Th…
Valuations on Convex Bodies and Functions
Monika Ludwig, Fabian Mussnig
An introduction to geometric valuation theory is given. The focus is on classification results for invariant and rigid motion invariant valuations on convex…
Affine fractional Sobolev inequalities
Julián Haddad, Monika Ludwig
Sharp affine fractional Sobolev inequalities for functions on are established. The new inequalities are stronger than (and directly imply) the sharp fractional…
Affine Fractional Sobolev and Isoperimetric Inequalities
Julián Haddad, Monika Ludwig
Sharp affine fractional Sobolev inequalities for functions on are established. For each , the new inequalities are significantly stronger than (and directly im…
The Hadwiger theorem on convex functions, IV: The Klain approach
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
New proofs of the Hadwiger theorem for smooth and for continuous valuations on convex functions are obtained, and the Klain-Schneider theorem on convex functions is established. In…
Geometric valuation theory
Monika Ludwig
A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.
The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A complete family of functional Steiner formulas is established. As applications, an explicit representation of functional intrinsic volumes using special mixed Monge-Ampère measur…
The Hadwiger theorem on convex functions, II: Cauchy-Kubota formulas
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A new version of the Hadwiger theorem on convex functions is established and an explicit representation of functional intrinsic volumes is found using new functional Cauchy-Kubota…
The Hadwiger theorem on convex functions, I
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on is established. Th…
A homogeneous decomposition theorem for valuations on convex functions
A. Colesanti, M. Ludwig, F. Mussnig
The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation inva…
Minkowski valuations on convex functions
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A classification of SL contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measur…
Tensor valuations on lattice polytopes
Monika Ludwig, Laura Silverstein
The Ehrhart polynomial and the reciprocity theorems by Ehrhart \& Macdonald are extended to tensor valuations on lattice polytopes. A complete classification is established of tens…
Valuations on Convex Functions
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
All continuous, SL and translation invariant valuations on the space of convex functions on are completely classified.
Weighted floating bodies and polytopal approximation
Florian Besau, Monika Ludwig, Elisabeth M. Werner
Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to estab…
Minkowski valuations on lattice polytopes
Karoly J. Boroczky, Monika Ludwig
A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over the integers and are translation invariant. In t…
Affine invariant valuations on polytopes
Monika Ludwig, Matthias Reitzner
A classification of SL invariant valuations on the space of convex polytopes in without any continuity assumptions is established. A corresponding result is obtained on…
Anisotropic Fractional Sobolev Norms
Monika Ludwig
Bourgain, Brezis & Mironescu showed that (with suitable scaling) the fractional Sobolev -seminorm of a function $f\in W^{1,p}(\rn)$ converges to the Sobolev seminorm of as $…
Anisotropic fractional perimeters
Monika Ludwig
The anisotropic fractional -perimeter with respect to a convex body in $\rn$ is shown to converge to the anisotropic perimeter with respect to the moment body of as $s\t…
General affine surface areas
Monika Ludwig
Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for affine s…
Elementary moves on triangulations
Monika Ludwig, Matthias Reitzner
It is proved that a triangulation of a polyhedron can always be transformed into any other triangulation of the polyhedron by using only elementary moves. One consequence is that a…