Related papers: Hill's level surfaces in the circular restricted t…
We study the asymptotic Plateau problem in $\BHH$ for area minimizing surfaces, and give a fairly complete solution for finite curves.
For a hyperbolic surface S of finite type we consider the set A(S) of angles between closed geodesics on S. Our main result is that there are only finitely many rational multiples of \pi in A(S).
In this paper, we build up Hill-type formula for linear Hamiltonian systems with Lagrangian boundary conditions, which include standard Neumann, Dirichlet boundary conditions. Such a kind of boundary conditions comes from the brake symmetry…
We study dynamical constraints arising from Embedded Contact Homology (ECH) in the spatial isosceles three-body problem. For energies below the critical level, the dynamics on the energy surface is identified with a Reeb flow on the tight…
Let Y be a surface with only finitely many singularities all of which are cusps. A set of cusps on Y is called three-divisible, if there is a cyclic global triple cover of Y branched precisely over these cusps. The aim of this note is to…
The restricted circular three-body problem is considered for the following parameter values $C=3.03$, $\mu=0.0009537$ - the values for {\em Oterma} comet in the Sun-Jupiter system. We present a computer assisted proof of an existence of…
Given a non circular spacial closed curve whose total torsion is an integer multiple of $2\pi$, we construct a germ of a smooth surface that contains it as a hyperbolic principal cycle.
We describe the equations of motion of elastodynamic bounded bodies in 3-space, and their linearizations at a stationary point. Using the latter as an approximation to model small motions, we develop a scheme to find numerical solutions of…
A polygonal surface in the pseudo-hyperbolic space H^(2,n) is a complete maximal surface bounded by a lightlike polygon in the Einstein universe Ein^(1,n) with finitely many vertices. In this article, we give several characterizations of…
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that…
This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds arise from varying hypotheses on the surface…
We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint locally geodesic segments. We prove that the flip graph of geometric triangulations with fixed vertices of a flat torus or a…
In this paper, continuing our previous work, we investigate the third gap problem in the Simon conjecture for closed minimal surfaces in the unit sphere. By developing refined third-order Simons-type integral identities and establishing new…
In this paper we study surfaces in R^3 that arise as limit shapes in a class of random surface models arising from dimer models. The limit shapes are minimizers of a surface tension functional, that is, they minimize, for fixed boundary…
We discuss the existence of equilibrium configurations for the Hamiltonian point-vortex model on a closed surface $\Sigma$. The topological properties of $\Sigma$ determine the occurrence of three distinct situations, corresponding to…
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain…
The nonlocal $s$-fractional minimal surface equation for $\Sigma= \partial E$ where $E$ is an open set in $R^N$ is given by $$ H_\Sigma^ s (p) := \int_{R^N} \frac {\chi_E(x) - \chi_{E^c}(x)} {|x-p|^{N+s}}\, dx \ =\ 0 \quad \text{for all }…
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of…
We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the…