Related papers: On the Cheeger problem for rotationally invariant …

In this paper we present some classification results for the steady Euler equations in two-dimensional exterior domains with free boundaries. We prove that, in an exterior domain, if a steady Euler flow devoid of interior stagnation points…

This paper is devoted to a complete characterization of the free boundary of all solutions to the following spectral $k$-partition problem with measure and inclusion constraints: \[ \inf \left\{\sum_{i=1}^k \lambda_1(\omega_i)\; : \;…

Weakly harmonic maps from a domain $\Omega$ (the upper half-space $\Rd$ or a bounded $C^{1,\alpha}$ domain, $\alpha\in (0,1]$) into a smooth closed manifold are studied. Prescribing small Dirichlet data in either of the classes…

In this paper we study sets in the $n$-dimensional Heisenberg group $\hhn$ which are critical points, under a volume constraint, of the sub-Riemannian perimeter associated to the distribution of horizontal vector fields in $\hhn$. We define…

We prove that for every $n \ge 2$, there exists a pseudoconvex domain $\Omega \subset \mathbb{C}^n$ such that $\mathfrak{c}^0(\Omega) \subsetneq \mathfrak{c}^1(\Omega)$, where $\mathfrak{c}^k(\Omega)$ denotes the core of $\Omega$ with…

Let $\Omega$ be an open, bounded domain in the plane with connected and smooth boundary, and $\omega$ an eigenfunction of the Neumann Laplacian corresponding to some Neumann eigenvalue $\mu > 0$. If the boundary value of $\omega$ is a…

We consider the Laplacian with attractive Robin boundary conditions, \[ Q^\Omega_\alpha u=-\Delta u, \quad \dfrac{\partial u}{\partial n}=\alpha u \text{ on } \partial\Omega, \] in a class of bounded smooth domains…

We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The…

The Leray transform and related boundary operators are studied for a class of convex Reinhardt domains in $\mathbb C^2$. Our class is self-dual; it contains some domains with less than $C^2$-smooth boundary and also some domains with smooth…

In this paper, we investigate an initial-boundary value problem for a chemotaxis-fluid system in a general bounded regular domain $\Omega \subset \mathbb{R}^N$ ($N\in\{2,3\}$), not necessarily being convex. Thanks to the elementary lemma…

We give a full classification of complete rotationally invariant surfaces with constant Gauss curvature in Berger spheres: they are either Clifford tori, which are flat, or spheres of Gauss curvature $K \geq K_0$ for a positive constant…

On compact Riemannian manifolds with a large isometry group we investigate the invariant spectrum of the ordinary Laplacian. For either a toric Kaehler metric, or a rotationally-symmetric metric on the sphere, we produce upper bounds for…

It is known that for $\Omega \subset \mathbb{R}^{2}$ an unbounded convex domain and $H>0$, there exists a graph $G\subset \mathbb{R}^{3}$ of constant mean curvature $H$ over $\Omega $ with $\partial G=$ $\partial \Omega $ if and only if…

We obtain a classification result for rotational surfaces in the Heisenberg space and the universal cover of the special linear group, whose mean curvature is given as a prescribed $C^1$ function depending on their angle function. We show…

In this paper, we study meromorphic functions on a domain $\Omega \subset \mathbb{C}$ whose image has finite spherical area, counted with multiplicity. The paper is composed of two parts. In the first part, we show that the limit of a…

Let $\Omega \subset \mathbb{C}^n$ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for $\Omega$ to be Reinhardt, complete Reinhardt, circular or Hartogs in terms of the orthogonality…

We give a negative answer to the rigidity conjecture of He and Schramm by constructing a rigid circle domain $\Omega$ on the Riemann sphere with conformally non-removable boundary. Here rigidity means that every conformal map from $\Omega$…

In this paper we analyze the problem of the geodesic connectedness of subsets of Riemannian manifolds. By using variational methods, the geodesic connectedness of open domains (whose boundaries can be not differentiable and not convex) of a…

We study the boundary limits of the Carath\'eodory and Kobayashi-Eisenman volume elements on smoothly bounded convex finite type domains and also on Levi corank one domains.

We investigate symmetric grain boundaries in a lamellar diblock copolymer system. The form of the interface between two grains strongly depends on the angle $\theta$, between the normals of the grains. When this angle is small, the lamellae…