Related papers: Rigidity theorems by capacities and kernels

In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR) Yamabe problem, Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on…

The Bergman theory of domains $\{ |{z_{1} |^{\gamma}} < |{z_{2}} | < 1 \}$ in $\mathbb{C}^2$ is studied for certain values of $\gamma$, including all positive integers. For such $\gamma$, we obtain a closed form expression for the Bergman…

We prove versions of the Suslin and Gabber rigidity theorems in the setting of equivariant pseudo pretheories of smooth schemes over a field with an action of a finite group. Examples include equivariant algebraic $K$-theory, presheaves…

We prove $\times a$ $\times b$ measure rigidity for multiplicatively independent pairs when $a\in\mathbb{N}$ and $b>1$ is a ``specified'' real number (the $b$-expansion of $1$ has a tail or bounded runs of $0$'s) under a positive entropy…

In this paper we pose and prove a spacetime version of Gromov's dihedral rigidity theorem (Gromov, Li) for cubes when the dimension is 3 by studying the level sets of spacetime harmonic functions (Stern, Bray-Stern, Hirsch-Kazaras-Khuri),…

Let X be a compact Riemann surface equipped with a real-analytic K\"ahler form $\omega$ and let E be a holomorphic vector bundle over $X$ equipped with a real-analytic Hermitian metric $h$. Suppose that the curvature of $h$ is…

We give a proof that every space of weighted square-integrable holomorphic functions admits an equivalent weight whose Bergman kernel has zeroes. Here the weights are equivalent in the sense that they determine the same space of holomorphic…

We exploit the equality of Bergman analytic content and torsional rigidity of a simply connected domain to develop a new method for calculating these quantities. This method is particularly suitable for the case when the region in question…

We prove that for any field k of characteristic p>0, any separated scheme X of finite type over k, and any overconvergent F-isocrystal E over X, the rigid cohomology H^i(X, E) and rigid cohomology with compact supports H^i_c(X,E) are finite…

On a two dimensional Stein space with isolated, normal singularities, smooth finite type boundary, and locally algebraic Bergman kernel, we establish an estimate on the type of the boundary in terms of the local algebraic degree of the…

There have been, over the last 8 years, a number of far reaching extensions of the famous original F. and M. Riesz's uniqueness theorem that states that if a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has the…

In this article we prove a differentiable rigidity result. Let $(Y, g)$ and $(X, g_0)$ be two closed $n$-dimensional Riemannian manifolds ($n\geqslant 3$) and $f:Y\to X$ be a continuous map of degree $1$. We furthermore assume that the…

We study stationary hollow vortices with surface tension in two dimensions. Such objects solve an overdetermined elliptic free boundary problem in an exterior domain, with an additional boundary condition involving mean curvature and the…

We study heat kernel rigidity for the Lie group $\operatorname{SU}\left( 2 \right)$ kernel equipped with a sub-Riemannian structure. We prove that a metric measure space equipped with a heat kernel of a special form is bundle-isometric to…

In his work on the mathematical formulation of 2d quantum gravity Schwarz established a rigidity result for Kac-Schwarz operators for the n-KdV hierarchies. Later on, Adler and van Moerbeke as well as Fastr\'{e} obtained different proofs of…

We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rank one isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube…

Let $X$ be a (data) set. Let $K(x,y)>0$ be a measure of the affinity between the data points $x$ and $y$. We prove that $K$ has the structure of a Newtonian potential $K(x,y)=\varphi(d(x,y))$ with $\varphi$ decreasing and $d$ a quasi-metric…

We prove that in a Riemannian manifold $M$, each function whose Hessian is proportional the metric tensor yields a weighted monotonicity theorem. Such function appears in the Euclidean space, the round sphere $S^n$ and the hyperbolic space…

For a once-punctured complex torus, we compare the Bergman kernel and the fundamental metric, by constructing explicitly the Evans-Selberg potential and discussing its asymptotic behaviors. This work aims to generalize the Suita type…

We take advantage of a rigidity result for the equation satisfied by an extremal function associated with a special case of the Caffarelli-Kohn-Nirenberg inequalities to get a symmetry result for a larger set of inequali-ties. The main…