Related papers: Sharp upper bounds on resonances for perturbations…

Perturbation expansions up to third order for the generalized spiked harmonic oscillator Hamiltonians H = -d^2/dx^2+ x^2 + A/x^2 + lambda/x^alpha, A >= 0, 2gamma > alpha, gamma=1+(1/2)sqrt(1+4A), and small values of the coupling lambda > 0,…

Let $M$ be a compact $n$-dimensional Riemannian manifold with nonnegative Ricci curvature and mean convex boundary $\partial M$. Assume that the mean curvature $H$ of the boundary $\partial M$ satisfies $H \geq (n-1) k >0$ for some positive…

We analyse the maximum achievable rate of sustained computation for a given convex region of three dimensional space subject to geometric constraints on power delivery and heat dissipation. We find a universal upper bound across both…

We generalize the Froissart-Martin upper bound for the scattering amplitude in spaces with compactified extra dimensions.

We prove rigidity results involving the Hawking mass for surfaces immersed in a $3$-dimensional, complete Riemannian manifold $(M,g)$ with non-negative scalar curvature (resp. with scalar curvature bounded below by $-6$). Roughly, the main…

We prove the existence of a resonance free region in scattering by a strictly convex obstacle with the Robin boundary condition. More precisely, we show that the scattering resonances lie below a cubic curve which is the same as in the case…

Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small perturbation approach. In the limiting case of a large correlation length…

The question of whether it is possible to compute scattering resonances of Schr\"odinger operators - independently of the particular potential - is addressed. A positive answer is given, and it is shown that the only information required to…

An exact trace formula for the perturbation of the Laplacian by a Dirac delta potential on a compact hyperbolic Riemann surface is derived. The formula can be considered an analogue of the Selberg trace formula. The difference of perturbed…

In this note, we consider semiclassical scattering on a manifold which is Euclidean near infinity or asymptotically hyperbolic. We show that, if the cut-off resolvent satisfies polynomial estimates in a strip of size $O(h |\log…

Let $\Lambda$ be a non-elementary convex co-compact fuchsian group which is a subgroup of an arithmetic fuchsian group. We prove that the Laplace operator of the hyperbolic surface $X=\Lambda \backslash\H$ has infinitely many resonances in…

If a real harmonic function inside the open unit disk $B(0,1) \subset \mathbb{R}^2$ has its level set $\left\{x: u(x) = u(0)\right\}$ diffeomorphic to an interval, then we prove the sharp bound $\kappa \leq 8$ on the curvature of the level…

In $\mathbb{R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimension of $k$-porous sets having holes of certain size near every point in $k$ orthogonal directions at all small scales. This bound tends to…

A central feature of quantum metrology is the possibility of Heisenberg scaling, a quadratic improvement over the limits of classical statistics. This scaling, however, is notoriously fragile to noise. While for some noise types it can be…

We prove that the lacunary spherical maximal operator, defined on the $n$-dimensional real hyperbolic space, is bounded on $L^p(\mathbb{H}^n)$ for all $n\ge2$ and $1<p\le\infty$. In particular, the lacunary set is significantly larger than…

We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative estimate showing that if the spectral gap of an RCD$(N-1,…

Physical theories have a limited regime of validity and hence must be accompanied by a breakdown diagnostic to establish when they cease to be valid as parameters are varied. For perturbative theories, estimates of the first neglected order…

The inscribed radius of a compact manifold with boundary is bounded above if its Ricci curvature and mean curvature are bounded from below. The rigidity result implies that the upper bound can be achieved only in space form. In this paper,…

In this paper, we consider a compact Riemannian manifold with boundary, endowed with a magnetic potential $\alpha$ and a potential $U$. For brevity, this type of systems are called $\MP$-systems. On simple $\MP$-systems, we consider both…

This paper derives a perturbation bound on the optimal subspace estimator obtained from a subset of its canonical projections contaminated by noise. This fundamental result has important implications in matrix completion, subspace…