Related papers: Boundary Value Problem and Discrete Schwarz-Pick L…
We prove the well-posedness of the initial boundary value problem for the Einstein equations with sole boundary condition the requirement that the timelike boundary is totally geodesic. This provides the first well-posedness result for this…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
We first prove a Boundary Schwarz lemma for holomorphic disks on the unit ball in $\mathbb{C}^n$. Further by using a Schwarz lemma for minimal conformal disks of Forstneri\v c and Kalaj (F.~Forstneri{\v{c}} and D.~Kalaj. \newblock…
The discontinuous Galerkin (DG) finite element method when applied to hyperbolic conservation laws requires the use of shock-capturing limiters in order to suppress unphysical oscillations near large solution gradients. In this work we…
This paper has two main objectives. First, for an arbitrary calibrated manifold $(X,\phi)$, we define notions of $R_\phi$-hyperbolicity and $\phi$-hyperbolicity, which respectively generalize the notions of Kobayashi and Brody hyperbolicity…
We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface. In the special case of a hyperbolic pair of pants, this settles a conjecture of Chas-Li-Maskit.
We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions which is constraint-preserving and sufficiently general to include…
We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex…
This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…
Two-phase composites with non-overlapping inclusions randomly embedded in matrix are investigated. A straight forward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value…
We extend the Gibbs conditioning principle to an abstract setting combining infinitely many linear equality constraints and non-linear inequality constraints, which need not be convex. A conditional large large deviation principle (LDP) is…
The main goal of this work is to prove that a very generic surface of degree at least 21 in complex projective 3-dimensional space is hyperbolic in the sense of Kobayashi. This means that every entire holomorphic map $f:{\Bbb C} \to X$ to…
H. L. Skala (1992) gave the first elegant first-order axiom system for hyperbolic geometry by replacing Menger's axiom involving projectivities with the theorems of Pappus and Desargues for the hyperbolic plane. In so doing, Skala showed…
We give upper-bounds for the dimension of some linear systems. The theorem improves the differential Horace method introduced by Alexander-Hirschowitz, and was conjectured by Simpson. Possible applications are the calculus of the dimension…
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on…
Boundary integral methods for the solution of boundary value PDEs are an alternative to `interior' methods, such as finite difference and finite element methods. They are attractive on domains with corners, particularly when the solution…
We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a…
With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…