A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The Stone-Weierstrass theorem aids in solving inverse problems on specific manifolds.
Relation between generalized Weierstrass representation for conformal immersion of generic surfaces into three-dimensional space and Lax-Phillips scattering theory for automorphic functions is considered.
We study relations of the Weierstrass's hyperelliptic al-functions over a non-degenerated hyperelliptic curve of arbitrary genus as solutions of sine-Gordon equation using Weierstrass's local parameters, which are characterized by two ramified points. Though the hyperelliptic solutions of the sine-Gord…
A space-like surface in Minkowski space-time is minimal if its mean curvature vector field is zero. Any minimal space-like surface of general type admits special isothermal parameters - canonical parameters. For any minimal surface of general type parameterized by canonical parameters we obtain Weierstrass representati…
A formula connects discrete harmonic surfaces to holomorphic functions.
We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a far more complete theory than one would expect from general elasticity theory. For some of these functionals elastic maps even admit a "Weier…
Let C be a hyperelliptic Riemann surface. We show that the hyperelliptic Weierstrass points of C are non-degenerated critical points of Morse index +2 of the curvature function K of the Theta metric on C (called also Bergman metric). When the genus of C is two, we compute all critical points of K and we show in this ca…
We prove that any minimal (maximal) strongly regular surface in the three-dimensional Minkowski space locally admits canonical principal parameters. Using this result, we find a canonical representation of minimal strongly regular time-like surfaces, which makes more precise the Weierstrass representation and shows mor…
Defines spherical type surfaces via support function and classifies them.
Generalized Weierstrass representations for generic surfaces conformally immersed into four-dimensional Euclidean and pseudo-Euclidean spaces of different signatures are presented. Integrable deformations of surfaces in these spaces generated by the Davey-Stewartson hierarchy of integrable equations are proposed. Willm…
New bound on neural nets complexity for approximating functions.
The paper finds a Weierstrass representation for a specific type of Lorentzian minimal surface.
New algorithm corrects bias in LDP-released data for better analysis.
This paper connects Laguerre minimal surfaces to Weierstrass representations.
New representations for discrete surfaces derived from dual transforms.
It is known that any maximal space-like surface without isotropic points in the four-dimensional pseudo-Euclidean space with neutral metric admits locally geometric parameters which are special case of isothermal parameters. With respect to such parameters the surface is determined uniquely up to a motion by the Gauss …
Solves natural PDEs for minimal Lorentz surfaces in 4D spacetime.
Functional input neural networks approximate continuous functions on weighted spaces.
Paper connects surfaces in 4D and 3D spacetime.
Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfaces are generated by the Davey -Stewartson hierarchy. Geometrically thes…
Minimal surfaces of general type in Euclidean 4-space are characterized with the conditions that the ellipse of curvature at any point is centered at this point and has two different principal axes. Any minimal surface of general type locally admits geometrically determined parameters - canonical parameters. In such pa…
Making use of Murakami's classification of outer involutions in a Lie algebra and following the Morse-theoretic approach to harmonic two-spheres in Lie groups introduced by Burstall and Guest, we obtain a new classification of harmonic two-spheres in outer symmetric spaces and a Weierstrass-type representation for such…
We give a simple, direct proof of the easy fact about the Weierstrass Representation, namely, that it always gives a minimal surface. Most presentations include the much harder converse that every simply connected minimal surface is given by the Weierstrass Representation.
New integrable systems for marginally trapped surfaces in 4D Lorentz-Minkowski space.
Short introduction to discrete flat fronts in hyperbolic space with a Weierstrass representation proof.
The paper examines the behavior of Weierstrass measures on stable curves as they approach a nodal stable curve.
The paper finds formulas for special surface shapes in 3D space.
In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass-Enneper representation, by using a system of hodographic coordinates. This is done by using the method of solving the Born-Infeld equations by Whitham. We directly compute conformal coordinates on the minimal surf…
A new approach is proposed for study structure and properties of the total squared mean curvature of surfaces in . It is based on the generalized Weierstrass formulae for inducing surfaces. The quantity (Willmore functional) is shown to be invariant under the modified Novikov--Veselov hierarchy of in…
For two generator free Fuchsian groups, the quotient three manifold is a genus two solid handlebody and its boundary is a hyperelliptic Riemann surface. The convex core is also a hyperelliptic Riemann surface. We find the Weierstrass points of both of these surfaces. We then generalize the notion of a hyperelliptic Rie…
This work extends holomorphic surface representations to isotropic space.
In the present paper which a sequel to dg-ga/9511005 and dg-ga//9610013 a global Weierstrass representation of an arbitrary closed oriented surface of genus in the the three-space is constructed. The Weierstrass spectrum of a torus immersed into is introduced and finite-zone planes as well as finite-zone…
With the rapidly growing scales of statistical problems, subset based communication-free parallel MCMC methods are a promising future for large scale Bayesian analysis. In this article, we propose a new Weierstrass sampler for parallel MCMC based on independent subsets. The new sampler approximates the full data poster…
The study connects minimal and maximal surfaces in 3D and 3-L space.
Paper provides a formula for translating solitons and singular minimal surfaces.
We give a explicit computation of the pointed harmonic volumes of hyperelliptic curves with Weierstrass base points, which are paraphrased into a combinatorial formula.
The paper extends Weierstrass representation to non-minimal conformal immersions.
We construct the spectral curve and the Baker--Akhiezer function for the Dirac operator which corresponds to the Clifford torus via the Weierstrass representation. By constructing this Baker--Akhiezer function we demonstrate a general procedure for constructing Dirac operators and their Baker--Akhiezer functions corres…
Unified representation for minimal and constant mean curvature surfaces.
The study of the relation between the Weierstrass inducing formulae for constant mean curvature surfaces and the completely integrable euclidean nonlinear sigma-model suggests a connection among integrable sigma -models in a background and other type of surfaces. We show how a generalization of the Weierstrass represen…
Weierstrass-type representations have been used extensively in surface theory to create surfaces with special curvature properties. In this paper we give a unified description of these representations in terms of classical transformation theory of -surfaces.
Quasiclassical generalized Weierstrass representation for highly corrugated surfaces with slow modulation in the three-dimensional space is proposed. Integrable deformations of such surfaces are described by the dispersionless Veselov-Novikov hierarchy.
The Weierstrass representation for spheres in and, in particular, effective construction of immersions from data of spectral theory origin is discussed. These data are related to Dirac operators on a plane and on an infinite cylinder and these operators are just representations of Dirac operators acting in spino…
Using the submanifold quantum mechanical scheme, the restricted Dirac operator in a submanifold is defined. Then it is shown that the zero mode of the Dirac operator expresses the local properties of the submanifold, such as the Frenet-Serret and generalized Weierstrass relations. In other words this article gives a re…
New method constructs translationally equivariant hyperbolic affine spheres.
The paper classifies affine minimal translation surfaces and finds their properties.
The abstract discusses parallels between Galois theory and Stone-Weierstrass theorem in various fields.
Generalizations of the Weierstrass formulae to generic surface immersed into , and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.