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A sharp stability estimate for tensor tomography in non-positive curvature
We consider the geodesic X-ray transform acting on solenoidal tensor fields on a compact simply connected manifold with strictly convex boundary and...
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Forward and Reverse Entropy Power Inequalities in Convex Geometry
The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski...
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Valuations on Convex Bodies and Functions
An introduction to geometric valuation theory is given. The focus is on classification results for...
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The Löwner Function of a Log-Concave Function
We introduce the notion of Löwner (ellipsoid) function for a log-concave function and show that it is an extension of the Löwner ellipsoid for convex...
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Log-Concave Functions
We attempt to provide a description of the geometric theory of log-concave functions. We present the main aspects of this theory: operations between...
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Hardy Spaces with Variable Exponents
In this paper, we make a survey on some recent developments of the theory of Hardy spaces with variable exponents in different settings.
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Dual Orlicz Mixed Affine Quermassintegrals
In this paper, a class of geometric quantities of star bodies via dual Orlicz mixed volumes are presented. It is proved that these geometric...
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An instability criterion for volume-preserving area-stationary surfaces with singular curves in sub-Riemannian 3-space forms
We study stable surfaces, i.e., second order minima of the area for variations of fixed volume, in sub-Riemannian space forms of dimension 3. We...
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Nonexistence of maximizers for the functional of the centroaffine Minkowski problem
The centroaffine Minkowski problem is studied, which is the critical case of the L p -Minkowski problem. It admits a variational structure that plays...
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The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem
In this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an...
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A discrete version of Koldobsky’s slicing inequality
Let # K be a number of integer lattice points contained in a set K . In this paper we prove that for each d ∈ N there exists a constant C ( d ) depending...
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Concepts Related to Constant Width
A polytope P is circumscribed about a convex body \(\phi \subset \mathbb {E}^n\)...
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L p -Dual Mixed Affine Surface Areas
Lutwak proposed the notion of L p -affine surface area corresponding to the notion of Lp -mixed volume. Recently,Wang and He introduced the concept of L ...
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Random ball-polyhedra and inequalities for intrinsic volumes
We prove a randomized version of the generalized Urysohn inequality relating mean width to the other intrinsic volumes. To do this, we introduce a...