Related papers: Strong Kato limit can be branching
Consider a $q$-ary block code satisfying the property that no $l$-letters long codeword's prefix occurs as a suffix of any codeword for $l$ inside some interval. We determine a general upper bound on the maximum size of these codes and a…
We prove that optimal lower eigenvalue estimates of Zhong-Yang type as well as a Cheng-type upper bound for the first eigenvalue hold on closed manifolds assuming only a Kato condition on the negative part of the Ricci curvature. This…
The {\em Singular Cardinal Hypothesis} (SCH) is one of the most classical combinatorial principles in set theory. It says that if $\kappa$ is singular strong limit, then $2^{\kappa}=\kappa^+$. We prove that given a singular cardinal…
In this paper we establish a weak and a strong law of large numbers for supercritical superprocesses with general non-local branching mechanisms. Our results complement earlier results obtained for superprocesses with only local branching.…
This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on $N$-dimensional ${\rm RCD}(K,N)$ spaces $(X,\mathsf{d},\mathscr{H}^N)$. Moreover, we obtain almost…
We show that for a strongly convergent sequence of purely loxodromic finitely generated Kleinian groups with incompressible ends, Cannon-Thurston maps, viewed as maps from a fixed base limit set to the Riemann sphere, converge uniformly.…
Typical existence result on Ricci-flat metrics is in manifolds of finite geometry, that is, on $F=\bar F-D$ where $\bar F$ is a compact K\"ahler manifold and $D$ is a smooth divisor. We view this existence problem from a different…
In this short note we survey theorems and provide conjectures on gluing constructions under lower curvature bounds in smooth and non-smooth context. Focusing on synthetic lower Ricci curvature bounds we consider Riemannian manifolds,…
We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $\mathrm{CAT}(\kappa)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in…
A weak formulation is devised for the K(m,n) equation which is a nonlinearly dispersive generalization of the gKdV equation having compacton solutions. With this formulation, explicit weak compacton solutions are derived, including ones…
In this article we develop a simplistic approach to revisit the classical Kato-Ponce inequality, which is also known as 'fractional Leibniz rule.' As a consequence, we derive the validity of this inequality even in quasi-Banach spaces $L^p$…
By extending Koiso's examples to the non-compact case, we construct complete gradient Kahler-Ricci solitons of various types on certain holomorphic line bundles over compact Kahler-Einstein manifolds. Moreover, a uniformization result on…
In this note, the idea of finite dimensional $L^p$ spaces is transferred to Lorentzian length spaces to provide an example that is locally nowhere Minkowskian. Looking at the sectional curvature bounds of this example leads to the more…
The Ricci iteration is a discrete analogue of the Ricci flow. We give the first study of the Ricci iteration on a class of Riemannian manifolds that are not K\"ahler. The Ricci iteration in the non-K\"ahler setting exhibits new phenomena.…
We consider the Kato and the Dynkin class and their local counterparts on a smooth Riemannian manifold as Fr\'{e}chet spaces. Based on recent results by Carron, Mondello and Tewodrose we show that for a Riemannian manifold $(X,g)$ of…
We prove sharp lower bounds for the charged Hawking mass of stable surfaces in electrostatic space-times in various contexts. An upper bound for the genus of stable surfaces in the electrostatic system is provided. We also study the…
We construct a continuous 3-parameter family of non-shrinking Ricci solitons complex line bundles $O(k)$ over $\mathbb{CP}^{2m+1}$, where the base space is not necessarily K\"ahler--Einstein. Each $O(k)$ with $k\in [3,2m+1]$ admits at least…
We present a criterion for deciding which compact extra dimensional spaces yield physically reliable Newton's law corrections. We study compact manifolds with boundary and without boundary. The boundary conditions which we use on the…
We study stability of non-compact gradient Kaehler-Ricci flow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kaehler…
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that for doubling spaces these are also…