Related papers: Width Stability of Rotationally Symmetric Metrics

We consider incompressible Euler equations in any dimension $ d\geq3 $ imposing axisymmetric symmetry without swirl. While the global regularity of smooth flows in this setting has been well-known in $ d=3 $, the same question in higher…

We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By ex- tending the least-squares stabilization to the overlap…

Our manuscript aims to analysis the viability and stability of anisotropic stellar objects in the modified symmetric teleparallel gravity. A particular model of this extended theory is considered to formulate explicit field equations which…

We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2…

Let $g$ be a complete, asymptotically flat metric on $\mathbb{R}^3$ with vanishing scalar curvature. Moreover, assume that $(\mathbb{R}^3,g)$ supports a nearly Euclidean $L^2$ Sobolev inequality. We prove that $(\mathbb{R}^3,g)$ must be…

We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…

Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability…

We define a flexible class of Riemmanian metrics on the three-torus. Then, using Stern's inequality relating scalar curvature to harmonic one-forms, we show that any sequence of metrics in this family whose negative part of the scalar…

In this note we consider two topics involving the relationship between the symplectic capacity and the mean width of convex bodies in $\mathbb{R}^{2n}$. We first describe an alternative path from the symplectic Brunn-Minkowski inequality of…

A regular class of static, cylindrically symmetric pure magnetic field metrics is rederived in a different metric ansatz in all dimensions. Radial, time dependent perturbations show that for dimensions d>3 such spacetimes are stable at both…

We study the set of volumes of constant scalar curvature one metrics on an atoroidal three-manifold.The infinum of this set is believed to be attained at a hyperbolic metric. We prove that the supremum of this set is always infinity. The…

E. Calabi and J. Cao showed that a closed geodesic of least length in a two-sphere with nonnegative curvature is always simple. Using min-max theory, we prove that for some higher dimensions, this result holds without assumptions on the…

In this work we construct a sequence of Riemannian metrics on the three-sphere with scalar curvature greater than or equal to $6$ and arbitrarily large widths. Our procedure is based on the connected sum construction of positive scalar…

In this paper, we are concerned with the global existence and stability of a 3-D perturbed viscous circulatory flow around an infinite long cylinder. This flow is described by 3-D compressible Navier-Stokes equations. By introducing some…

We prove stability estimates for the isoperimetric inequalities for the first and the second nonzero Laplace eigenvalues on surfaces, both globally and in a fixed conformal class. We employ the notion of eigenvalues of measures and show…

The existence of two geometrically distinct closed geodesics on an $n$-dimensional sphere $S^n$ with a non-reversible and bumpy Finsler metric was shown independently by Duan--Long [7] and the author [27]. We simplify the proof of this…

Using the calculus of variations, we prove the following structure theorem for noise stable partitions: a partition of $n$-dimensional Euclidean space into $m$ disjoint sets of fixed Gaussian volumes that maximize their noise stability must…

We prove that in a closed Riemannian manifold with dimension between $3$ and $7$, either there are minimal hypersurfaces with arbitrarily large area, or there exist uncountably many stable minimal hypersurfaces. Moreover, the latter case…

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to…

Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the…