Related papers: Lipschitz Shadowing for Flows

We study the behavior of the Cheeger isoperimetric constant under the Ricci flow on compact surfaces. For metrics on a surface diffeomorphic to $S^2$, we show that the Cheeger constant is non-decreasing along the flow. The proof uses…

We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain $\Omega $ in ${\mathbb{R}}^N$. We consider deformations $\phi (\Omega)$ of $\Omega $ obtained by means of a locally Lipschitz…

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…

We show stability of pairs of Ricci flat metrics and parallel spinor fields with respect to the spinor flow, i.e. we show that the spinor flow with initial conditions near such pairs converges to a critical point with exponential speed.…

Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…

In this paper we prove the linear stability of a gauge-modified version of the Bach flow on any complete manifold (M, h) of constant curvature. This involves some intricate calculations to obtain spectral bounds, and in particular…

Recent studies of pseudo-plane ideal flow (PIF) reveal a ubiquitous presence of vortex alignment in both homogeneous and stratified fluids, and in both inertial and rotating reference frames as well. The exact solutions of a steady-state…

This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two…

The classical fluid dynamics boundary condition of no-slip suggests that variation in the wettability of a solid should not affect the flow of an adjacent liquid. However experiments and molecular dynamics simulations indicate that this is…

Morphological instability of the solid-liquid interface occuring in a crystal growing from an undercooled thin liquid being bounded on one side by a free surface and flowing down inclined plane is investigated by a linear stability analysis…

We study the stability of closed, not necessarily smooth, equilibrium surfaces of an anisotropic surface energy for which the Wulff shape is not necessarily smooth. We show that if the Cahn Hoffman field can be extended continuously to the…

Let $\left(X_n, d_n\right)$ be a sequence of metric spaces and let $\mathcal{F}=\left\{f_n\right\}_{n \in \mathbb{Z}}$ be a sequence of continuous and onto maps $f_n: X_n \rightarrow X_{n+1}, n \in \mathbb{Z}_{+}$. In this paper, we prove…

The asymptotic stability of two-dimensional stationary flows in a non-symmetric exterior domain is considered. Under the smallness condition on initial perturbations, we show the stability of the small stationary flow whose leading profile…

Let M be a non-orientable compact 2-manifold of genus 4. Then there exists a family of quasi-minimal, Kupka-Smale smooth vector fields X_r in M, depending smoothly on 0<=r<e, such that, for some flow box V in M of X_0, and for all 0<=r,v<e,…

We explore the characteristics of shadows for a general class of spherically symmetric, static spacetimes, which may arise in general relativity or in modified theories of gravity. The chosen line element involves a sum (with constant but…

Representation stability is a phenomenon whereby the structure of certain sequences $X_n$ of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^2$ with Lipschitz boundary or a bounded convex domain in $\mathbb{C}^n$ and $\phi\in C(\overline{\Omega})$ such that $H_{\phi}$ is compact on $A^2(\Omega)$. Then $\phi\circ f$ is…

We prove that the reconstruction of a certain type of length spaces from their travel time data on a closed subset is Lipschitz stable. The travel time data is the set of distance functions from the entire space, measured on the chosen…

We derive the most general flux-induced superpotential for N=1 M-theory compactifications on seven-dimensional manifolds with SU(3) structure. Imposing the appropriate boundary conditions, this result applies for heterotic M-theory. It is…

We consider a unique continuation problem for the wave equation given data in a volumetric subset of the space time domain. In the absence of data on the lateral boundary of the space-time cylinder we prove that the solution can be…