Related papers: A non-concentration estimate for partially rectang…

We consider a space of $L^2$ vector fields with bounded mean oscillation whose ``normal'' component to the boundary is well-controlled. In the case when the dimension $n \geq 3$, we establish its Helmholtz decomposition for arbitrary…

On any compact Riemannian manifold $(M, g)$ of dimension $n$, the $L^2$-normalized eigenfunctions ${\phi_{\lambda}}$ satisfy $||\phi_{\lambda}||_{\infty} \leq C \lambda^{\frac{n-1}{2}}$ where $-\Delta \phi_{\lambda} = \lambda^2…

We discuss a special class of Beltrami coefficients whose associated quasiconformal mapping is bilipschitz. These are of the form the characteristic function of a planar bounded domain with smooth boundary of class C 1+epsilon times a…

In this paper, we define what is called a quasi-Reinhardt domain and study biholomorphisms between such domains. We show that all biholomorphisms between two bounded quasi-Reinhardt domains fixing the origin are polynomial mappings, and we…

We provide the rigorous justification of the NLS approximation, in Sobolev regularity, for a class of quasilinear Hamiltonian Klein Gordon equations with quadratic nonlinearities on large one-dimensional tori $\T_L:=\mathbb{R}/(2\pi L…

For a large class of semiclassical pseudodifferential operators, including Schr\"odinger operators, $ P (h) = -h^2 \Delta_g + V (x) $, on compact Riemannian manifolds, we give logarithmic lower bounds on the mass of eigenfunctions outside…

I present a class of theories that generalize quasilinear MOND (QUMOND). Like QUMOND, these GQUMOND theories require solving only the linear Poisson equation (twice). Unlike QUMOND, their Lagrangian depends on higher derivatives of the…

A concrete lower-bound for the Hochschild cohomological dimension of a commutative $k$-algebra, in terms of three other homological invariants is obtained. This result is then used to show that most $k$-algebras fail to be quasi-free, even…

The Schr\"odinger equation in a square or rectangle with hard walls is solved in every introductory quantum mechanics course. Solutions for other polygonal enclosures only exist in a very restricted class of polygons, and are all based on a…

Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue \lambda. We show that the volume of {f>0} inside any ball B whose center lies on {f=0} is >…

In this paper we show that in some cases the E.Hopf rigidity phenomenon admits quantitative interpretation. More precisely we estimate from above the measure of the set $\mathcal{M}$ swept by minimal orbits. These estimates are sharp, i.e.…

We study the $\bar{\partial}_b$-Neumann problem for domains $\Omega$ contained in a strictly pseudoconvex manifold M^{2n+1} whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts…

We prove estimates for solutions of the $\bar \partial u=\omega $ equation in a strictly pseudo convex domain $ \Omega $ in ${\mathbb{C}}^{n}.$ For instance if the $ (p,q)$ current $\omega $ has its coefficients in $L^{r}(\Omega )$ with…

In this article we study the well-posedness of the Boltzmann equation near its hydrodynamic limit on a bounded domain. We consider two types of domains, namely $C^2$ domains with Maxwell boundary conditions where the accommodation…

We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in $\mathbb{R}^n$, $n\ge 2$, for classes of semilinear and quasilinear conductivity equations,…

We prove that the spaces of smooth and ultradifferentiable vectors associated with a representation of a real Lie group on a Fr\'{e}chet space $E$ are quasinormable if $E$ is so. A similar result is shown to hold for the linear topological…

We prove that a a strongly convex planar domain (Birkhoff table) with dihedral symmetry, which is sufficiently close in a finitely smooth topology to an ellipse, is deformationally spectrally rigid within the class of domains preserving…

We prove that for any semi-Dirichlet form $(\epsilon, D(\epsilon))$ on a measurable Lusin space $E$ there exists a Lusin topology with the given $\sigma$-algebra as the Borel $\sigma$-algebra so that $(\epsilon, D(\epsilon))$ becomes…

A variational inequality for the images of $k$-dimensional hyperplanes under quasiconformal maps of the $n$-dimensional Euclidean space is proved when $1\le k\le n-2 .$

We show that for almost every $(P,\lambda)$ where $P$ is a convex polygon and $\lambda\in(0,1)$, the corresponding outer billiard about $P$ with contraction $\lambda$ is asymptotically periodic, i.e., has a finite number of periodic orbits…