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pro vyhledávání: '"Alesker, Semyon"'
Autor:
Alesker, Semyon
In the last two decades a number of structures on the classical space of translation invariant valuations on convex bodies were discovered, e.g. product, convolution, a Fourier type transform. In this paper a non-Archimedean analogue of the space of
Externí odkaz:
http://arxiv.org/abs/2401.09131
Autor:
Alesker, Semyon, Gordon, Peter
A new class of Riemannian metrics, called octonionic K\"ahler, is introduced and studied on a certain class of 16-dimensional manifolds. It is an octonionic analogue of K\"ahler metrics on complex manifolds and of HKT-metrics of hypercomplex manifold
Externí odkaz:
http://arxiv.org/abs/2212.07857
Let $\{X_i\}$ be a sequence of compact $n$-dimensional Alexandrov spaces (e.g. Riemannian manifolds) with curvature uniformly bounded below which converges in the Gromov-Hausdorff sense to a compact Alexandrov space $X$. In an earlier paper by the fi
Externí odkaz:
http://arxiv.org/abs/2204.13018
Autor:
Alesker, Semyon
In 1939 H. Weyl has introduced the so called intrinsic volumes $V_i(M^n), i=0,\dots,n$, (known also as Lipschitz-Killing curvatures) for any closed smooth Riemannian manifold $M^n$. Given a Riemmanian submersion of compact smooth Riemannian manifolds
Externí odkaz:
http://arxiv.org/abs/2105.12590
Autor:
Alesker, Semyon
Very recently J. Kotrbaty has proven general inequalities for translation invariant smooth valuations formally analogous to the Hodge- Riemann bilinear relations in the Kahler geometry. The goal of this note is to apply Kotrbaty's theorem to obtain a
Externí odkaz:
http://arxiv.org/abs/2010.01859
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Autor:
Alesker, Semyon
The notion of a valuation on convex bodies is very classical. The notion of a valuation on a class of functions was recently introduced and studied by M. Ludwig and others. We study an explicit relation between continuous valuations on convex functio
Externí odkaz:
http://arxiv.org/abs/1703.08778
Autor:
Alesker, Semyon
For any closed smooth Riemannian manifold H. Weyl has defined a sequence of numbers called today intrinsic volumes. They include volume, Euler characteristic, and integral of the scalar curvature. We conjecture that absolute values of all intrinsic v
Externí odkaz:
http://arxiv.org/abs/1611.09546
Autor:
Alesker, Semyon, Bernig, Andreas
Publikováno v:
Journal of Differential Geometry, 107 (2017), 203-240
We introduce the new notion of convolution of a (smooth or generalized) valuation on a group $G$ and a valuation on a manifold $M$ acted upon by the group. In the case of a transitive group action, we prove that the spaces of smooth and generalized v
Externí odkaz:
http://arxiv.org/abs/1507.04851