Zobrazeno 1 - 10
of 23
pro vyhledávání: '"52A20, 52B45"'
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:
Faifman, Dmitry
We investigate the support of a distribution $f$ on the real grassmannian $\mathrm{Gr}_k(\mathbb R^n)$ whose spectrum, namely its nontrivial $\mathrm O(n)$-components, is restricted to a subset $\Lambda$ of all $\mathrm O(n)$-types. We prove that unl
Externí odkaz:
http://arxiv.org/abs/2201.11734
Publikováno v:
Math. Ann. 381(2021), 1615-1652
We show the existence of additive kinematic formulas for general flag area measures, which generalizes a recent result by Wannerer. Building on previous work by the second named author, we introduce an algebraic framework to compute these formulas ex
Externí odkaz:
http://arxiv.org/abs/2003.13262
Autor:
Li, Jin, Leng, Gangsong
Publikováno v:
Adv. Math. 299 (2016) 139-173
For $1 \leq p < \infty$, Ludwig, Haberl and Parapatits classified $L_p$ Minkowski valuations intertwining the special linear group with additional conditions such as homogeneity and continuity. In this paper,a complete classification of $L_p$ Minkows
Externí odkaz:
http://arxiv.org/abs/1802.07561
Publikováno v:
J. Funct. Anal. 272 (2017), no. 2, 738-758
It is proved that the classical Laplace transform is a continuous valuation which is positively GL$(n)$ covariant and logarithmic translation covariant. Conversely, these properties turn out to be sufficient to characterize this transform.
Externí odkaz:
http://arxiv.org/abs/1802.07563
Autor:
Hug, Daniel, Schneider, Rolf
Publikováno v:
Communications in Contemporary Mathematics (2016) 1650061 (31 pages)
For valuations on convex bodies in Euclidean spaces, there is by now a long series of characterization and classification theorems. The classical template is Hadwiger's theorem, saying that every rigid motion invariant, continuous, real-valued valuat
Externí odkaz:
http://arxiv.org/abs/1606.06028
Autor:
Hug, Daniel, Schneider, Rolf
The Minkowski tensors are valuations on the space of convex bodies in ${\mathbb R}^n$ with values in a space of symmetric tensors, having additional covariance and continuity properties. They are extensions of the intrinsic volumes, and as these, the
Externí odkaz:
http://arxiv.org/abs/1605.00954
Autor:
Abardia, Judit, Gómez, Eugenia Saorín
The difference body operator enjoys different characterization results relying on its basic properties such as continuity, SL(n)-covariance, Minkowski valuation or symmetric image. The Rogers-Shephard and the Brunn-Minkowski inequalities provide uppe
Externí odkaz:
http://arxiv.org/abs/1602.00967
Autor:
Abardia, Judit, Gómez, Eugenia Saorín
Publikováno v:
Communications in Contemporary Mathematics, Vol. 17, No. 4, 1450023, 32 pp., 2015
We investigate geometrical properties and inequalities satisfied by the complex difference body, in the sense of studying which of the classical ones for the difference body have an analog in the complex framework. Among others we give an equivalent
Externí odkaz:
http://arxiv.org/abs/1602.00960
Autor:
Li, Jin, Leng, Gangsong
Publikováno v:
Indiana Univ. Math. J., 66 (2017), no.3, 791--819
In this paper, Orlicz valuations compatible with $SL(n)$ transforms are classified. Unlike their $L_p$ analogs, the identity operator and the reflection operator are the only $SL(n)$ compatible Orlicz valuations (up to dilations). It turns out that t
Externí odkaz:
http://arxiv.org/abs/1510.04511