Joscha Prochno,Daniel Rudolf
Joscha Prochno
We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy in (Anz Österreich Akad Wiss Math Nat Kl 132:3-10, 1995). In particular, we see that the inverse N(ε,d) ...
Steen Markvorsen,Matteo Raffaelli
Steen Markvorsen
We study totally umbilic isometric immersions between Riemannian manifolds. First, we provide a novel characterization of the totally umbilic isometric immersions with parallel normalized mean curvature vector, i.e., those having nonzero me...
Brunn-Minkowski Inequality for [Formula: see text]-Convolution Bodies via Ball's Bodies [0.03%]
Ball's体的[公式见正文]-卷积体上的Brunn-Minkowski不等式
David Alonso-Gutiérrez,Javier Martín Goñi
David Alonso-Gutiérrez
We consider the problem of finding the best function φn:[0,1]→R such that for any pair of convex bodies K,L∈Rn the following Brunn-Minkowski type inequality holds |K+θL|1n≥φn(θ)(|K|1n+|L|1n),where K+	...
Enrico Le Donne,Daniele Morbidelli,Séverine Rigot
Enrico Le Donne
In this paper, we introduce the notion of horizontally affine, h-affine in short, function and give a complete description of such functions on step-2 Carnot algebras. We show that the vector space of h-affine functions on the free step-2 r...
Volker Branding
Volker Branding
This article is concerned with the stability of triharmonic maps and in particular triharmonic hypersurfaces. After deriving a number of general statements on the stability of triharmonic maps we focus on the stability of triharmonic hypers...
Leandro Arosio,Gian Maria Dall&#x;Ara,Matteo Fiacchi
Leandro Arosio
We show that Worm domains are not Gromov hyperbolic with respect to the Kobayashi distance. Keywords: Gromov...
The Topological State Derivative: An Optimal Control Perspective on Topology Optimisation [0.03%]
拓扑状态导数：拓扑优化的最优控制视角
Phillip Baumann,Idriss Mazari-Fouquer,Kevin Sturm
Phillip Baumann
In this paper, we introduce the topological state derivative for general topological dilatations and explore its relation to standard optimal control theory. We show that for a class of partial differential equations, the shape-dependent st...
Antonio Lerario,Francesca Tripaldi
Antonio Lerario
The aim of this paper is to give a thorough insight into the relationship between the Rumin complex on Carnot groups and the spectral sequence obtained from the filtration on forms by homogeneous weights that computes the de Rham cohomology...
Szegő Kernel Asymptotics on Complete Strictly Pseudoconvex CR Manifolds [0.03%]
完备严格伪凸CR流形上的Szegö核渐近性理论
Chin-Yu Hsiao,George Marinescu,Huan Wang
Chin-Yu Hsiao
We prove a Bochner-Kodaira-Nakano formula and establish Szegő kernel expansions on complete strictly pseudoconvex CR manifolds with transversal CR R -action under certain natural geometric conditions. As a consequence we show that such man...
Stefan Haller
Stefan Haller
We propose an analytic torsion for the Rumin complex associated with generic rank two distributions on closed 5-manifolds. This torsion behaves as expected with respect to Poincaré duality and finite coverings. We establish anomaly formula...