Zobrazeno 1 - 10
of 165
pro vyhledávání: '"Ye, Deping"'
We calculate the first order variation of the Riesz $\alpha$-energy of a log-concave function $f$ with respect to the Asplund sum. Such a variational formula induces the Riesz $\alpha$-energy measure of log-concave function $f$, which will be denoted
Externí odkaz:
http://arxiv.org/abs/2408.16141
The central focus of this paper is the $L_p$ dual Minkowski problem for $C$-compatible sets, where $C$ is a pointed closed convex cone in $\mathbb{R}^n$ with nonempty interior. Such a problem deals with the characterization of the $(p, q)$-th dual cu
Externí odkaz:
http://arxiv.org/abs/2404.09804
The variation of a class of Orlicz moments with respect to the Asplund sum within the class of log-concave functions is demonstrated. Such a variational formula naturally leads to a family of dual Orlicz curvature measures for log-concave functions.
Externí odkaz:
http://arxiv.org/abs/2309.12260
Schneider introduced an inter-dimensional difference body operator on convex bodies and proved an associated inequality. In the prequel to this work, we showed that this concept can be extended to a rich class of operators from convex geometry and pr
Externí odkaz:
http://arxiv.org/abs/2305.17468
For a convex body $K$ in $\mathbb R^n$, the inequalities of Rogers-Shephard and Zhang, written succinctly, are $$\text{vol}_n(DK)\leq \binom{2n}{n} \text{vol}_n(K) \leq \text{vol}_n(n\text{vol}_n(K)\Pi^\circ K).$$ Here, $DK=\{x\in\mathbb R^n:K\cap(K+
Externí odkaz:
http://arxiv.org/abs/2305.00479
In 1970, Schneider generalized the difference body of a convex body to higher-order, and also established the higher-order analogue of the Rogers-Shephard inequality. In this paper, we extend this idea to the projection body, centroid body, and radia
Externí odkaz:
http://arxiv.org/abs/2304.07859
This paper is dedicated to study the sine version of polar bodies and establish the $L_p$-sine Blaschke-Santal\'{o} inequality for the $L_p$-sine centroid body. The $L_p$-sine centroid body $\Lambda_p K$ for a star body $K\subset\mathbb{R}^n$ is a co
Externí odkaz:
http://arxiv.org/abs/2206.00185
Let $C$ be a pointed closed convex cone in $\mathbb{R}^n$ with vertex at the origin $o$ and having nonempty interior. The set $A\subset C$ is $C$-coconvex if the volume of $A$ is finite and $A^{\bullet}=C\setminus A$ is a closed convex set. For $0
Externí odkaz:
http://arxiv.org/abs/2204.00860
We extend the notion of Ulam floating sets from convex bodies to Ulam floating functions. We use the Ulam floating functions to derive a new variational formula for the affine surface area of log-concave functions.
Externí odkaz:
http://arxiv.org/abs/2203.09563
Publikováno v:
In Journal of Functional Analysis 15 January 2025 288(2)
