Related papers: Local spectral convergence in $RCD^*(K,N)$ spaces

We identify a regularity property for structured ring spectra, and with it we prove a natural analogue of Quillen's localization theorem for algebraic K-theory in this setting.

We provide a sufficient condition for sets of mobile sampling in terms of the surface density of the set.

In this work, we will introduce and study the notion of local randomness for compact metric groups. We prove a mixing inequality as well as a product result for locally random groups under an additional dimension condition on the volume of…

We study the problem of whether the curvature-dimension condition with negative values of the generalized dimension parameter is stable under a suitable notion of convergence. To this purpose, first of all we introduce an appropriate…

In this paper, we prove a stability result for the non-K\"ahler geometry of locally conformally K\"ahler (lcK) spaces with singularities. Specifically, we find sufficient conditions under which the image of an lcK space by a holomorphic…

We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative estimate showing that if the spectral gap of an RCD$(N-1,…

We consider an $N$-soliton solution of the focusing nonlinear Schr\"{o}dinger equations. We give conditions for the synchronous collision of these $N$ solitons. When the solitons velocities are well separated and the solitons have equal…

It was shown by Mondino-Wei that any $\mathrm{RCD}^{*}(K,N)$ space $(X,d,\mathfrak{m})$ has a universal cover. We prove that for any point $x \in X$ and $R>0$, there exists $r<R$ such that any loop in $B_r(x)$ is contractible in $B_R(x)$;…

We prove a spectral inequality for Schr\"odinger equations with power growth potentials, which particularly confirms a conjecture in \cite{DSV}. This spectral inequality depends on the decaying density of the sensor sets, and the growth…

In a previous article, we introduced a reduction procedure for locally conformally symplectic manifolds at any regular value of the momentum mapping. We use this construction to prove an analogue of a well-known theorem in the symplectic…

We establish the boundary regularity of harmonic maps from $RCD(K, N)$ metric measure spaces into $CAT(0)$ metric spaces.

We consider a homogeneous space $X=(X,d,m) $ of dimension $\nu\geq1$ and a local regular Dirichlet form in $L^{2}(X,m) .$ We prove that if a Poincar\'{e} inequality holds on every pseudo-ball $B(x,R) $ of $X$, then an Harnack's inequality…

Strong theorems are given for the maximal local time on balls and subspaces for the $d$-dimensional simple symmetric random walk.

We give a sufficient condition for the local limit theorem. To construct it, we employ infinite times of convolutions of probability density functions.

In this paper, we have introduced first the notion of rough $I^*$-convergence in a normed linear space as an extension work of rough $I$-convergence and then rough $I^K$-convergence in more general way. Then we have studied some properties…

We show that several different interpretations of the inequality $\Delta f\leq\eta$ are equivalent in the setting of $\mathrm{RCD}(K,N)$ spaces. With respect to previously available results in this direction, we improve both on the…

In this paper we prove almost sure convergence to the ball, in the Nikodym metric, of sequences of random Steiner symmetrizations of bounded Caccioppoli and bounded measurable sets, paralleling a result due to Mani-Levitska concerning…

In this paper, for an immersion $f$ of an $n$-dimensional Riemannian manifold $M$ into $(n+d)$-Euclidean space we give a sufficient condition on $f$ so that, in case $d\leq 5$, any immersion $g$ of $M$ into $(n+d+1)$-Euclidean space that…

In this paper, we shall explore the Mosco convergence on regular subspaces of one-dimensional irreducible and strongly local Dirichlet forms. We find that if the characteristic sets of regular subspaces are convergent, then their associated…

A theoretical description of local absorption is proposed in order to investigate spectral variations on a length scale comparable with the extension of the relevant quantum states. A general formulation is derived within the density-matrix…