Related papers: Torus Solutions to the Weierstrass-Enneper Represe…
Using different forms of the arithmetic Riemann-Roch theorem and the computations of Bott-Chern secondary classes, we compute the analytic torsion and the height of Hirzebruch surfaces.
The Moutard transform is constructed for the solutions of the Davey-Stewartson II equation. It is geometrically interpreted using the spinor (Weierstrass) representation of surfaces in four-dimensional Euclidean space. Using the Moutard…
A general recipe is developed for the study of rigid body dynamics in terms of Poincar\'e surfaces of section. A section condition is chosen which captures every trajectory on a given energy surface. The possible topological types of the…
A new range of uniform $L^p$ resolvent estimates is obtained in the setting of the flat torus, improving previous results of Bourgain, Shao, Sogge and Yao. The arguments rely on the $\ell^2$-decoupling theorem and multidimensional Weyl sum…
The eigenvalues and a series representation of the eigenfunctions of the Schrodinger equation for a particle on the surface of a torus are derived.
We construct embeddings of Kauffman bracket skein algebras of surfaces (either closed or with boundary) into localized quantum tori using the action of the skein algebra on the skein module of the handlebody. We use those embeddings to…
We prove that formal WKB solutions of Schr\"odinger equations on Riemann surfaces are resurgent. Specifically, they are Borel summable in almost all directions and their Borel transforms admit endless analytic continuation away from a…
Let X be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2. The main result of this paper is a finite presentation of the 2-torsion in the Brauer group of X with…
We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its…
This paper deals with the exact solutions of a nonlinear coupled coupled wave equation. The (G'/G)-expansion method has been applied to derive kink solutions and singular wave solutions. The restrictions on the coefficients of the governing…
We show that a properly designed bianisotropic metasurface placed at the interface between two arbitrary different media, or coating a dielectric medium exposed to the air, provides Brewster (reflectionless) transmission at arbitrary angles…
We employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation. The implicit expression of smooth soliton solutions is given. The explicit…
We initiate the study of torus surgeries on knot traces. Our key technical insight is realizing the annulus twisting construction of Osoinach as a torus surgery on a knot trace. We present several applications of this idea. We find exotic…
Weihrauch reducibility is a notion of reducibility between computational problems that is useful to calibrate the uniform computational strength of a multivalued function. It complements the analysis of mathematical theorems done in reverse…
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the generalized Brethenton equation are given.
Calculation of the universal enveloping TROs of continuous JBW$*-triples, and application of the techniques used to supplement the structural results of Ruan for W*-TROs.
The paper develops a continiuty method for solutions of the Abreu equation, which include extremal metrics on toric surfaces. Results are obtained, assuming a hypothesis (the "M-condition") on the solutions.
We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions…
We solve the Cauchy problem for the $n$-dimensional wave equation using elementary properties of the Bessel functions.
Developing deep learning techniques for geometric data is an active and fruitful research area. This paper tackles the problem of sphere-type surface learning by developing a novel surface-to-image representation. Using this representation…