Simon Blatt,Matteo Raffaelli
Simon Blatt
We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in R3 can be extended to an infinitely narrow flat ribbon having minimal bending energy. We also show that, in general, minimizers are not free...
The [Formula: see text] Condition, [Formula: see text]-Approximators, and Varopoulos Extensions in Uniform Domains [0.03%]
[公式：见正文中]-条件、[公式：见正文中]-近似值和均匀域中的Varopoulos延拓
S Bortz,B Poggi,O Tapiola et al.
S Bortz et al.
Suppose that Ω⊂Rn+1, n≥1, is a uniform domain with n-Ahlfors regular boundary and L is a (not necessarily symmetric) divergence form elliptic, real, bounded operator in Ω. We show that the corresponding elliptic measur...
Completeness and Geodesic Distance Properties for Fractional Sobolev Metrics on Spaces of Immersed Curves [0.03%]
分数Sobolev度量下浸入曲线空间的完备性与测地线距离性质
Martin Bauer,Patrick Heslin,Cy Maor
Martin Bauer
We investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we consider are Sobolev metrics of possible fractional-order q∈[0,∞). We establish the ...
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...