相关论文: The fundamental gap of simplices

We extend to higher codimension earlier characterization of the equatorial disk and the critical catenoid by a pinching condition on the length of their second fundamental form among free boundary minimal surfaces in the three dimensional…

We prove that a stable minimal hypersurface of an open ball having a singular set of locally finite codimension 2 Hausdorff measure which is weakly close to a multiplicity 2 hyperplane is a 2-valued C^{1, alpha} graph in the interior.…

A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural…

We prove an effective variant of the Kazhdan-Margulis theorem generalized to stationary actions of semisimple groups over local fields: the probability that the stabilizer of a random point admits a non-trivial intersection with a small…

We provide a characterization of the radii minimal projections of polytopes onto $j$-dimensional subspaces in Euclidean space $\E^n$. Applied on simplices this characterization allows to reduce the computation of an outer radius to a…

We prove an inequality that generalizes the Fan-Taussky-Todd discrete analog of the Wirtinger inequality. It is equivalent to an estimate on the spectral gap of a weighted discrete Laplacian on the circle. The proof uses a geometric…

G\'alvez-Carrillo, Kock, and Tonks constructed a decomposition space $U$ of all M\"obius intervals, as a recipient of Lawvere's interval construction for M\"obius categories, and conjectured that $U$ enjoys a certain universal property: for…

We define various formal moduli spaces of p-divisible groups which are regular, and morphisms between them. We formulate arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture of the third author…

We study a generalization of the Erd\H{o}s-Falconer distance problem over finite fields. For a graph $G$, two embeddings $p, p': V(G) \to \mathbb{F}_q^d$ of a graph $G$ are congruent if for all edges $(v_i, v_j)$ of $G$ we have that…

We prove that a bounded open set U in Euclidean n-space has k-width less than C(n) Volume(U)^{k/n}. Using this estimate, we give lower bounds for the k-dilation of degree 1 maps between certain domains in Euclidean space. In particular, we…

\noindent Let $A$ be an arbitrary $C^*$ algebra. In \cite{BH} Blackadar and Handelman conjectured the set of lower semicontinuous dimension functions on $A$ to be pointwise dense in the set $DF(A)$ of all dimension functions on $A$ and…

In this paper, we show that under a mild condition, a principal submodule of the Bergman module on a bounded strongly pseudoconvex domain with smooth boundary in $\mathbb{C}^n$ is $p$-essentially normal for all $p>n$. This improves a…

We survey structure-preserving discretizations of minimal surfaces in Euclidean space. Our focus is on a discretization defined via parallel face offsets of polyhedral surfaces, which naturally leads to a notion of vanishing mean curvature…

Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg…

In this paper, we define a new capacity which allows us to control the behaviour of the Dirichlet spectrum of a compact Riemannian manifold with boundary, with "small" subsets (which may intersect the boundary) removed. This result…

The objective of this paper is two-fold. First, we establish new sharp quantitative estimates for Faber-Krahn inequalities on simply connected space forms. We prove that the gap between the first eigenvalue of a given set $\Omega$ and that…

A flip is a minimal move between two triangulations of a polytope. An open question is whether any two triangulations of the product of two simplices can be connected through a series of flips. This was proven in the case where one of the…

We investigate the geometric properties of simplices in Euclidean d-dimensional space for which two or more of the analogues of the classical triangle centers (including the centroid, circumcenter, incenter, orthocenter or Monge point, and…

In this note we establish several versions of a compactness theorem for submanifolds. In particular we require only bounds on the second fundamental form and do not assume volume or diameter bounds. As an application we prove a compactness…