Related papers: A note on Cheeger's isoperimetric constant
This paper is devoted to a deep analysis of the process known as Cheeger deformation, applied to manifolds with isometric group actions. Here, we provide new curvature estimates near singular orbits and present several applications. As the…
We prove that the isoperimetric constant is positive for all symmetric spaces of noncompact type and compute it explicitly.
We define a new Cheeger-like constant for graphs and we use it for proving Cheeger-like inequalities that bound the largest eigenvalue of the normalized Laplace operator.
A sharp quantitative polygonal isoperimetric inequality is obtained.
Let $(M^{n+1},g_+)$ be an asymptotically hyperbolic manifold. We compute the Cheeger constant of conformally compact asymptotically constant mean curvature submanifolds $ \iota : Y^{k+1} \to (M^{n+1},g_+)$ with arbitrary codimension. As an…
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
In this paper we introduce a Cheeger-type constant defined as a minimization of a suitable functional among all the $N$-clusters contained in an open bounded set $\Omega$. Here with $N$-Cluster we mean a family of $N$ sets of finite…
We improve constants in the Rademacher-Menchov inequality.
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
In this note we briefly survey and propose some open problems related to isoparametric theory.
We present in this work a new and simple proof of the false centre theorem.
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
We prove a formula for the intersection R-torsion of a finite cone and use it to introduce a family of spectral invariants which is closely related to Cheeger's half torsion.
Recently, in the metric spaces, Le Donne and the author introduced the so-called intrinsically Lipschitz sections. The main aim of this note is to adapt Cheeger theory for the classical Lipschitz constants in our new context. More…
The purpose of this note is to give the full and self-contained proof of Shchepin's result on a spectral representation of retracts of cubes.
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.
We prove a stability version of the isodiametric inequality on the sphere and in the hyperbolic space.
The graph Cheeger constant and Cheeger inequalities are generalized to the case of hypergraphs whose edges have the same cardinality. In particular, it is shown that the second largest eigenvalue of the generalized normalized Laplacian is…