Related papers: Quasiclassical generalized Weierstrass representat…
We propose Quadratic Gaussian Splatting (QGS), a novel representation that replaces static primitives with deformable quadric surfaces (e.g., ellipse, paraboloids) to capture intricate geometry. Unlike prior works that rely on Euclidean…
In this paper, we obtain Weierstrass representations for discrete constant mean curvature surfaces in isotropic 3-space, and use this to construct examples with discrete closed-form parametrizations.
We apply the invariant theory of surfaces in the four-dimensional Euclidean space to the class of general rotational surfaces with meridians lying in two-dimensional planes. We find all minimal super-conformal surfaces of this class.
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.
It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal Whitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane. Examples of deformations of…
In this paper, we study generalized constant ratio (GCR) hypersurfaces in Euclidean spaces. We mainly focus on the hypersurfaces in $\mathbb E^4$. First, we deal with $\delta(2)$-ideal GCR hypersurfaces. Then, we study on hypersurfaces with…
Demoulin surfaces in real projective $3$-space are investigated. Our result enable us to establish a generalized Weierstrass type representation for definite Demoulin surfaces by virtue of primitive maps into a certain semi-Riemannian…
We construct new integrable systems to present Weierstrass type representations for spacelike surfaces whose mean curvature vector $\mathbf{H}$ satisfies the null condition $\langle \mathbf{H}, \mathbf{H} \rangle=0$ in the four dimensional…
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…
We give a generalized Weierstrass formula for a Lorentz surface conformally immersed in the four-dimensional space $\mathbb{R}^{2,2}$ using spinors and Lorentz numbers. We also study the immersions of a Lorentzian surface in {\bf the}…
Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane…
The purpose of this short note is to relate a representation formula due to the Author and P. Romon for Lagrangian surfaces (see math.DG/0009202) to a more general Weierstrass representation type formula found by Konopelchenko for surfaces…
Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete Weierstrass-type representations of certain surface classes…
In this paper we define and analyze singularities of discrete linear Weingarten surfaces with Weierstrass-type representations in $3$-dimensional Riemannian and Lorentzian spaceforms. In particular, we discuss singularities of discrete…
A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and…
In this paper we provide a Weierstrass representation formula for translating solitons and singular minimal surfaces in ${\mathbb{R}^3}$. As application we study when the euclidean Gauss map has a harmonic argument and solve a general…
This paper addresses the problem of dynamic scene surface reconstruction using Gaussian Splatting (GS), aiming to recover temporally consistent geometry. While existing GS-based dynamic surface reconstruction methods can yield superior…
We compute the Lie symmetry algebra of the generalized Davey-Stewartson (GDS) equations and show that under certain conditions imposed on parameters in the system it is infinite-dimensional and isomorphic to that of the standard integrable…
Basic quantities related to 2-D gravity, such as Polyakov extrinsic action, Nambu-Goto action, geometrical action, and Euler characteristic are studied using generalized Weierstrass-Enneper (GWE) inducing of surfaces. Connection of the GWE…
Using the fact that any minimal strongly regular surface carries locally canonical principal parameters, we obtain a canonical representation of these surfaces, which makes more precise the Weierstrass representation in canonical principal…