Related papers: A note on Cheeger's isoperimetric constant

In a previous paper, the author proved the existence of extremal function for the Moser-Trudinger inequality on a compact manifold. In the this paper, we will give a new proof of one of the key proposition.

A very simple but useful almost sure convergence theorem of probability is given.

We investigate isoperimetric constants of infinite tessellating metric graphs. We introduce a curvature-like quantity, which plays the role of a metric graph analogue of discrete curvature notions for combinatorial tessellating graphs. We…

We give an extension of Cheeger's deformation techniques for smooth Lie group actions on manifolds to the setting of singular Riemannian foliations induced by Lie groupoids actions. We give an explicit description of the sectional curvature…

We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite graphs. Our proof proposes a new spectral clustering…

In this paper we study the relationship of hyperbolicity and (Cheeger) isoperimetric inequality in the context of Riemannian manifolds and graphs. We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying…

We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.

It was proved by Almgren that among boundaries whose mean curvature is bounded from above, perimeter is uniquely minimized by balls. We obtain sharp stability estimates for Almgren's isoperimetric principle and, as an application, we deduce…

We prove Cheeger-Gromov convergence for a subsequence of a given sequence of manifolds-with-boundary of bounded geometry. The method of the proof is to reduce, via height functions, the problem to the setting of Hamilton's compactnes…

In this paper, we provide a concrete interpretation of equivariant Reidemeister torsion and demonstrate that Bismut-Zhang's equivariant Cheeger-M\"{u}ller theorem simplifies considerably when applied to locally symmetric spaces. In a…

We show a simple way of deriving the Casimir Polder interaction, present some general arguments on the finiteness and sign of mutual Casimir interactions and finally we derive a simple expression for Casimir radiation from small accelerated…

The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type…

We present a new, elementary, dynamical proof of the prime number theorem.

Let $G$ be a group and let $X$ be a finite subset. The isoperimetric method investigates the objective function $|(XB)\setminus X|$, defined on the subsets $X$ with $|X|\ge k$ and $|G\setminus (XB)|\ge k$. A subset with minimal where this…

We give a short proof of Stein's universal multiplier theorem, purely by probabilistic methods, thus avoiding any use of harmonic analysis techniques (complex interpolation or transference methods).

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

We produce a new, shorter construction of a minor-universal planar graph.

We prove stability in the affirmative part of the Busemann-Petty problem on sections of complex convex bodies.

We present an elementary proof for Ljunggren equation

We study Cheeger and $p$-eigenvalue partition problems depending on a given evaluation function $\Phi$ for $p\in[1,\infty)$. We prove existence and regularity of minima, relations among the problems, convergence, and stability with respect…