Related papers: A note on the quantum Wielandt inequality

Korn's inequalities show that the $L^2$-norm of $\nabla u$ can be controlled by the $L^2$-norm of $\mathrm{Sym}(\nabla u)$, which only has $d(d+1)/2$ components. In [J. Math. Pures Appl. 148 (2021), pp. 199-220] Chipot posed the question of…

An integral is defined on the plane that includes the Henstock--Kurzweil and Lebesgue integrals (with respect to Lebesgue measure). A space of primitives is taken as the set of continuous real-valued functions $F(x,y)$ defined on the…

The three dimensional primitive equations with full viscosity are considered in a horizontally periodic box $\Omega$, which are subject to either the homogeneous Neumann or Dirichlet conditions on the upper and bottom parts of the boundary.…

We extend work of the first author concering relative double commutants and approximate double commutants of unital subalgebras of unital C*-algebras, including metric versions involving distance estimates. We prove metric results for AH…

The intuitive notion of the Gromov invariant for maps from a Riemann surface to a Grassmannian is shown to agree with the definition in \cite{BDW}. Also, an induction on the genus is proved, which extends the results of \cite{BDW} to a…

In 1996 Erdoes showed that among planar domains of fixed area, the smallest principal eigenvalue of the Dirichlet Laplacian with a constant magnetic field is uniquely achieved on the disk. We establish a quantitative version of this…

We present two sharp, closed-form empirical Bernstein inequalities for symmetric random matrices with bounded eigenvalues. By sharp, we mean that both inequalities adapt to the unknown variance in a tight manner: the deviation captured by…

Given a connected Riemannian manifold $\mathcal{N}$, an \(m\)--dimensional Riemannian manifold $\mathcal{M}$ which is either compact or the Euclidean space, $p\in [1, +\infty)$ and $s\in (0,1]$, we establish, for the problems of…

We observe that the $2$-norm distance $d_{U,2}$ between the unitary orbits of normal elements in a $\mathrm{II}_1$ factor $\mathcal{M}$ is equal to the $2$-Wasserstein distance between the spectral measures induced by the trace…

We extend the classical Schwarz-Pick inequality to the class of harmonic mappings between the unit disk and a Jordan domain with given perimeter. It is intriguing that the extremals in this case are certain harmonic diffeomorphisms between…

For every $g\geq 2$ we distinguish real period matrices of real Riemann surfaces of topological type $(g,0,0)$ from the ones of topological type $(g,k,1)$, with $k$ equal to one or two for $g$ even or odd respectively (Theorem B). To that…

Let $X$ be a closed, connected, oriented surface of genus $g$, with a hyperbolic metric chosen at random according to the Weil--Petersson measure on the moduli space of Riemannian metrics. Let $\lambda_1=\lambda_1(X)$ bethe first non-zero…

The Topological Tverberg Theorem claims that any continuous map of a (q-1)(d+1)-simplex to \R^d identifies points from q disjoint faces. (This has been proved for affine maps, for d=1, and if q is a prime power, but not yet in general.) The…

Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps…

We study the first nonzero Steklov eigenvalue $\lambda_2(T,\delta\Omega)$ of the Dirichlet-to-Neumann operator on a finite tree $T$ with leaf boundary $\delta\Omega$, under a constraint on the diameter $D$. He and Hua [Calc. Var. PDE, 2022]…

We prove that for any open Riemann surface $N,$ natural number $n\geq 3,$ non-constant harmonic map $h:N\to \mathbb{R}^{n-2}$ and holomorphic 2-form $H$ on $N,$ there exists a weakly complete harmonic map $X=(X_j)_{j=1,\ldots,n}:N \to…

I present several applications of the Dirac inequality to the determination of isolated unitary representations and associated "spectral gaps" in the case of unramified principal series. The method works particularly well in order to attach…

This work is motivated by a paper of Davenport and Schmidt, which treats the question of when Dirichlet's theorems on the rational approximation of one or of two irrationals can be improved and if so, by how much. We consider a…

A hereditarily atomic von Neumann algebra $A$ is a $W^*$ product of matrix algebras, regarded as the underlying function algebra of a quantum set. Projections in $A\overline{\otimes}A^{\circ}$ are interpreted as quantum binary relations on…

A K-quasiconformal selfmap of the unit disk with identity boundary values satisfies the H\"older estimate $|f(z)-f(w)| \leq 4^{1-1/K} |z-w|^{1/K}$. The constant $4^{1-\frac{1}{K}}$ is sharp.