Related papers: On Partial Smoothness, Tilt Stability and the $\ma…

A famous result of Jurgen Moser states that a symplectic form on a compact manifold cannot be deformed within its cohomology class to an inequivalent symplectic form. It is well known that this does not hold in general for noncompact…

Tilt stability plays a pivotal role in understanding how local solutions of an optimization problem respond to small, targeted perturbations of the objective. Although quadratic bundles are a powerful tool for capturing second-order…

One of the major problems in the theory of the porous medium equation is the regularity of the solutions and the free boundaries. Here we assume flatness of the solution in space time cylinder and derive smoothness of the interface after a…

This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…

Bridgeland stability manifolds of Calabi-Yau categories are of noticeable interest both in mathematics and in physics. By looking at some of the known example, a pattern clearly emerges and gives a fairly precise description of how they…

Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…

The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…

We define a Fr\'echet topology on the space $C^\infty(X)[[\hbar]]$ of formal smooth functions on a symplectic manifold $X$, by constructing a sequence of semi-norms on it. For any star product $\star$ on $C^\infty(X)[[\hbar]]$ making it a…

A very short proof of the following smooth homogeneity theorem of D. Repovs, E. V. Scepin and the author is presented. Let N be a locally compact subset of a smooth manifold M. Assume that for each two points x,y in N there exist their…

Let $X$ be a smooth compact manifold and $v$ a vector field on $X$ which admits a smooth function $f: X \to \mathbf R$ such that $df(v) > 0$. Let $\partial X$ be the boundary of $X$. We denote by $C^\infty(X)$ the algebra of smooth…

For any $Q\in\{\frac{3}{2},2,\frac{5}{2},3,\dotsc\}$, we establish a structure theory for the class $\mathcal{S}_Q$ of stable codimension 1 stationary integral varifolds admitting no classical singularities of density $<Q$. This theory…

Let K be the function field of a connected regular scheme S of dimension 1, and let f : X -> Y be a finite cover of projective smooth and geometrically connected curves over K with g(X) greater or equal to 2. Suppose that f can be extended…

In this note, we describe the possible singularities on a stable surface which is in the boundary of the moduli space of surfaces isogenous to a product. Then we use the $\mathbb Q$-Gorenstein deformation theory to get some connected…

For $p\in [1,\infty]$, we define a smooth manifold structure on the set $AC_{L^p}([a,b],N)$ of absolutely continuous functions $\gamma\colon [a,b]\to N$ with $L^p$-derivatives for all real numbers $a<b$ and each smooth manifold $N$ modeled…

We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only…

A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalise this result to moduli spaces of submanifolds of higher…

We show that any Lipschitz projection-valued function p on a connected closed Riemannian manifold can be approximated uniformly by smooth projection-valued functions q with Lipschitz constant close to that of p. This answers a question of…

Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…

Given a triangulated category $\mathcal{C}$, we construct a partial compactification, denoted $\mathcal{A}\mathrm{Stab}(\mathcal{C})$, of the quotient of its stability manifold by $\mathbb{C}$. The purpose of…

The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…