Related papers: A note on Aubin-Lions-Dubinskii lemmas
The above title is the same, but with "semisimple" instead of "simple," as that of a notice by N. Kowalsky. There, she announced many theorems on the subject of actions of simple Lie groups preserving a Lorentz structure. Unfortunately, she…
We show a stability result for the recently established Brunn--Minkowski inequality in compact simple Lie groups. Namely, we prove that if two compact subsets $A, B$ of a compact simple Lie group $G$ satisfy $$ \mu(AB)^{1/d'} \leq (1 +…
This article discusses a unified convergence analysis of the semilinear time-dependent equation $\partial_t u + (-1)^\mathrm{m}\Delta^{\mathrm{m}}u + u^3 - u = f$ with $\mathrm{m} \in \{1,2\}$ and homogeneous Dirichlet boundary conditions.…
In the first part of this paper, we give a new analytical proof of a theorem of C. Sabbah on integrable deformations of meromorphic connections on $\mathbb P^1$ with coalescing irregular singularities of Poincar\'e rank 1, and generalizing…
We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic…
We consider a notion of exact sequences in any -not necessarily exact- pointed category relative to a given (E;M)-factorization structure. We apply this notion to introduce and investigate a new notion of exact sequences of semimodules over…
We prove an intrinsic equivalence between strong hypercontractivity and a strong logarithmic Sobolev inequality for the cone of logarithmically subharmonic functions. We introduce a new large class of measures, Euclidean regular and…
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…
In this article we use techniques developed by Hrushovski-Loeser to study certain metric properties of the Berkovich analytification of a finite morphism of smooth connected projective curves. In recent work, M. Temkin proved a radiality…
The regularity of refinable functions has been studied extensively in the past. A classical result by Daubechies and Lagarias states that a compactly supported refinable function in $\R$ of finite mask with integer dilation and translations…
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…
The author was recently able to provide a cohomological interpretation of Tate's Riemann-Roch formula for number fields using some new harmonic analysis objects, ghost-spaces. When trying to investigate these objects in general, we realized…
The ADM mass, viewed as a functional on the space of asymptotically flat Riemannian metrics of nonnegative scalar curvature, fails to be continuous for many natural topologies. In this paper we prove that lower semicontinuity holds in…
Two specific families of distributions in harmonic and Clifford analysis are further studied through a spherical co-ordinates approach. In particular actions involving spherical co-ordinates, such as the radial derivative and the…
This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of…
Cousin's lemma is a compactness principle that naturally arises when studying the gauge integral, a generalisation of the Lebesgue integral. We study the axiomatic strength of Cousin's lemma for various classes of functions, using Friedman…
A series of detailed quantitative results is established for the family of demi-distributions which is a large extension of the family of usual distributions.
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent…
We prove a Liouville type theorem for entire maximal $m$-subharmonic functions in $\mathbb C^n$ with bounded gradient. This result, coupled with a standard blow-up argument, yields a (non-explicit) a priori gradient estimate for the complex…
In this paper we bring into attention variable coefficient cubic-quintic nonlinear Schr\"odinger equations which admit Lie symmetry algebras of dimension four. Within this family, we obtain the reductions of canonical equations of…