Zobrazeno 1 - 10
of 145
pro vyhledávání: '"Colesanti, Andrea"'
In this paper, we study new extensions of the functional Blaschke-Santalo inequalities, and explore applications of such new inequalities beyond the classical setting of the standard Gaussian measure.
Externí odkaz:
http://arxiv.org/abs/2409.11503
We prove that the first (nontrivial) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator $$ L(u)=\Delta u-\langle\nabla u,x\rangle\,, $$ as a function of the domain, is convex with respect to the Minkowski addition, and we characterize the equali
Externí odkaz:
http://arxiv.org/abs/2407.21354
We show that every continuous and dually translation invariant valuation on the space of Lipschitz functions on the unit sphere of $\mathbb{R}^n$, $n\ge2$, can be decomposed uniquely into a sum of homogeneous valuations of degree $0$, $1$ and $2$. In
Externí odkaz:
http://arxiv.org/abs/2401.05913
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
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
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere $S^{n-1}$. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded with respec
Externí odkaz:
http://arxiv.org/abs/2005.05419
We provide an integral representation for continuous, rotation invariant and dot product invariant valuations defined on the space Lip$(S^{n-1})$ of Lipschitz continuous functions on the unit $n-$sphere.
Comment: 27 pages
Comment: 27 pages
Externí odkaz:
http://arxiv.org/abs/1906.04118
Publikováno v:
Advances in Applied Mathematics 111 (2019), 1-29
An Orlicz version of the $L_p$-Minkowski problem on $S^{n-1}$ is discussed corresponding to the case $-n
Externí odkaz:
http://arxiv.org/abs/1812.05213