Martijn Kluitenberg
Martijn Kluitenberg
We generalize the Cheeger inequality, a lower bound on the first nontrivial eigenvalue of a Laplacian, to the case of geometric sub-Laplacians on rank-varying Carnot-Carathéodory spaces and we describe a concrete method to lower bound the ...
On the Dimension of the Singular Set of Perimeter Minimizers in Spaces with a Two-Sided Bound on the Ricci Curvature [0.03%]
具有双面有界里奇曲率的空间中周长极小元的奇异集的维数问题
Alessandro Cucinotta,Francesco Fiorani
Alessandro Cucinotta
We show that the Hausdorff dimension of the singular set of perimeter minimizers in noncollapsed limits of manifolds with two-sided bounds on the Ricci curvature is at most n - 5 , where n is the dimension of the ambient space. The estimat...
On the Isoperimetric and Isodiametric Inequalities and the Minimisation of Eigenvalues of the Laplacian [0.03%]
关于等周不等式与等直径不等式以及拉普拉斯算子特征值的极小化问题
Sam Farrington
Sam Farrington
We consider the problem of minimising the k-th eigenvalue of the Laplacian with some prescribed boundary condition over collections of convex domains of prescribed perimeter or diameter. It is known that these minimisation problems are well...
Albert Boggess,Jennifer Brooks,Andrew Raich
Albert Boggess
CR functions on an embedded quadric M always extend holomorphically to M + i Γ M where Γ M is the closure of the convex hull of the image of the Levi form. When Γ M is a closed polygonal cone, we show that the Bergman ker...
Efficient and Accurate Separable Models for Discretized Material Optimization: A Continuous Perspective Based on Topological Derivatives [0.03%]
基于拓扑导数的离散材料优化连续模型的有效且准确的分离模型
Peter Gangl,Nico Nees,Michael Stingl
Peter Gangl
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models constructe...
Harry Fluck,Xiaolong Li
Harry Fluck
This article aims to understand the behavior of the curvature operator of the second kind under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature operator of the second kind explicitly in terms of that of...
Volker Branding
Volker Branding
In this note we prove the existence of two proper biharmonic maps between the Euclidean ball of dimension bigger than four and Euclidean spheres of appropriate dimensions. We will also show that, in low dimensions, both maps are unstable cr...
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 ...