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

Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this…

We show that if the rotation set of a homeomorphism of the torus is stable under small perturbations of the dynamics, then it is a convex polygon with rational vertices. We also show that such homeomorphisms are $C^0$-generic and have…

For an integral $2$-varifold $V\subset \mathbb{S}^3$ with square-integrable mean curvature, unit density, and support of genus at least $1$, assume that its Willmore energy satisfies \[ \mathcal{W}(V)\le 2\pi^2+\delta^2,\qquad…

A subset of Euclidean space will be said to be $n$-smooth if it has an $n$-dimensional tangent plane at each of its points. Let ${\frak d}_n$ denote the least number $n$-smooth sets into which $n+1$-dimensional Euclidean space can be…

We construct tilt stability conditions on surface root stacks and show that they have support property with respect to the rational Chen-Ruan cohomology.

Let $X$ be a smooth projective variety. Define a stable map $f:C\to X$ to be "eventually smoothable" if there is an embedding $X\hookrightarrow\mathbb{P}^N$ such that $(C,f)$ occurs as the limit of a $1$-parameter family of stable maps to…

Let $N$ be a smooth $(n+l)$-dimensional Riemannian manifold. We show that if $V$ is an area-stationary union of three or more $C^{1,\mu}$ $n$-dimensional submanifolds-with-boundary $M_k \subset N$ with a common boundary $\Gamma$, then…

We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region $U$ can be swept out by a…

This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near…

We define a notion for unfolding smooth, ruled surfaces, and prove that every smooth prismatoid (the convex hull of two smooth curves lying in parallel planes), has a nonoverlapping "volcano unfolding." These unfoldings keep the base…

We define cusp-decomposable manifolds and prove smooth rigidity within this class of manifolds. These manifolds generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume,…

We provide a general framework for the stability of solutions to stochastic partial differential equations with respect to perturbations of the drift. More precisely, we consider stochastic partial differential equations with drift given as…

A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which…

Let $X$ be a normal complex space such that the tangent sheaf $T_X$ is locally free and locally admits a basis consisting of pairwise commuting vector fields. Then $X$ is smooth.

We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is…

We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions. We prove a result to the effect that these are stable under…

This article is devoted to the Relativistic Vlasov-Maxwell system in space dimension three. We prove the local smooth solvability for weak topologies (and its long time version for small data). This result is derived from a representation…

We describe a natural decomposition of a normal complex surface singularity $(X,0)$ into its "thick" and "thin" parts. The former is essentially metrically conical, while the latter shrinks rapidly in thickness as it approaches the origin.…

Incompressible flows of an ideal two-dimensional fluid on a closed orientable surface of positive genus are considered. Linear stability of harmonic, i.e. irrotational and incompressible, solutions to the Euler equations is shown using the…

In this paper we prove two theorems. The first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) in a homogeneously regular Riemannian three-manifold, in any…