Zobrazeno 1 - 10
of 213
pro vyhledávání: '"Ludwig, Monika"'
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. The valuations are classified in terms of their behaviour with respect t
Externí odkaz:
http://arxiv.org/abs/2407.07691
Autor:
Ludwig, Monika, Mussnig, Fabian
Publikováno v:
In: Convex Geometry: Cetraro, Italy 2021, Lecture Notes in Mathematics 2332, CIME Foundation subseries, pp. 19-78, Springer, Cham, 2023
An introduction to geometric valuation theory is given. The focus is on classification results for $\operatorname{SL}(n)$ invariant and rigid motion invariant valuations on convex bodies and on convex functions.
Externí odkaz:
http://arxiv.org/abs/2302.00416
Autor:
Haddad, Julián, Ludwig, Monika
Sharp affine Hardy--Littlewood--Sobolev inequalities for functions on $\mathbb R^n$ are established, which are significantly stronger than (and directly imply) the sharp Hardy--Littlewood--Sobolev inequalities by Lieb and by Beckner, Dou, and Zhu. In
Externí odkaz:
http://arxiv.org/abs/2212.12194
Autor:
Haddad, Julián, Ludwig, Monika
Publikováno v:
Math. Ann. 388 (2024), 1091-1115
Sharp affine fractional $L^p$ Sobolev inequalities for functions on $\mathbb R^n$ are established. The new inequalities are stronger than (and directly imply) the sharp fractional $L^p$ Sobolev inequalities. They are fractional versions of the affine
Externí odkaz:
http://arxiv.org/abs/2209.10540
Autor:
Haddad, Julián, Ludwig, Monika
Sharp affine fractional Sobolev inequalities for functions on $\mathbb R^n$ are established. For each $0
Externí odkaz:
http://arxiv.org/abs/2207.06375
Publikováno v:
Advances in Mathematics 413 (2023), 108832
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 addition, an extension theorem for valuations defined on functions wi
Externí odkaz:
http://arxiv.org/abs/2201.11565
Autor:
Ludwig, Monika
Publikováno v:
In: European Congress of Mathematics. Proceedings of the 8th Congress (8ECM). EMS Press, Berlin, 2023
A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.
Externí odkaz:
http://arxiv.org/abs/2111.09024
Publikováno v:
Calc. Var. Partial Differential Equations 61 (2022), 181
A complete family of functional Steiner formulas is established. As applications, an explicit representation of functional intrinsic volumes using special mixed Monge-Amp\`ere measures and a new version of the Hadwiger theorem on convex functions are
Externí odkaz:
http://arxiv.org/abs/2111.05648
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 formulas. In addition, connections between functional intrinsic volume
Externí odkaz:
http://arxiv.org/abs/2109.09434
Publikováno v:
Geometric and Functional Analysis 34 (2024), no. 6, 1839-1898
A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\mathbb R}^n$ is established. The valuations obtained are functional versions of the classical intrins
Externí odkaz:
http://arxiv.org/abs/2009.03702