Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Mussnig, Fabian"'
We prove a functional version of the additive kinematic formula as an application of the Hadwiger theorem on convex functions together with a Kubota-type formula for mixed Monge-Amp\`ere measures. As an application, we give a new explanation for the
Externí odkaz:
http://arxiv.org/abs/2403.06697
Motivated by a problem for mixed Monge-Amp\`ere measures of convex functions, we address a special case of a conjecture of Schneider and show that for every convex body $K$ the support of the mixed area measure $S(K[j],B_L^{n-1}[n-1-j],\cdot)$ is giv
Externí odkaz:
http://arxiv.org/abs/2401.16371
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
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
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
Autor:
Li, Ben, Mussnig, Fabian
Publikováno v:
Int. Math. Res. Not. IMRN 2022, no. 18, 14496-14563
We introduce a class of functional analogs of the symmetric difference metric on the space of coercive convex functions on $\mathbb{R}^n$ with full-dimensional domain. We show that convergence with respect to these metrics is equivalent to epi-conver
Externí odkaz:
http://arxiv.org/abs/2010.12846
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
Autor:
Mussnig, Fabian
Publikováno v:
Canadian Journal of Mathematics 73 (2021), 108-130
All non-negative, continuous, $\operatorname{SL}(n)$ and translation invariant valuations on the space of super-coercive, convex functions on $\mathbb{R}^n$ are classified. Furthermore, using the invariance of the function space under the Legendre tr
Externí odkaz:
http://arxiv.org/abs/1903.04225
Publikováno v:
In Advances in Mathematics 15 January 2023 413
