arXiv research

Real analytic solutions found for special Lagrangian equation.

Real analyticity proved for modified Laplacian coflow solutions.

It is a theorem of S. Bando that if $g(t)$ is a solution to the Ricci flow on a compact manifold $M$, then $(M, g(t))$ is real-analytic for each $t >0$. In this note, we extend his result to smooth solutions on open domains $U\subset M$.

Study classifies non-removable singularities in Minkowski 3-space equations.

Proves time analyticity for heat and Navier-Stokes equations without decaying conditions.

Let $\varphi(t), t\in [0,T]$ be a smooth solution to the Laplacian flow for closed G_2 structures on a compact 7-manifold $M$. We show that for each fixed positive time $t\in (0,T]$, $(M,\varphi(t),g(t))$ is real analytic, where $g(t)$ is the metric induced by $\varphi(t)$. Consequently, any Laplacian soliton is real a…

Analyzes solutions to non-elliptic equations on bounded domains.

Study proves convergence of quantized geodesics to Mabuchi geodesics.

In this paper, we prove that if $g(t)$ is a smooth, complete solution to the Ricci flow of uniformly bounded curvature on $M\times[0, Ω]$, then the correspondence $t\mapsto g(t)$ is real-analytic at each $t_0\in (0, Ω)$. The analyticity is a consequence of classical Bernstein-type estimates on the temporal and spatial …

Let $\mathcal{M}_1$ denote the space of solutions $z(x,y)$ to an elliptic, real analytic Monge-Ampère equation ${\rm det} (D^2 z)=\varphi(x,y,z,Dz)>0$ whose graphs have a non-removable isolated singularity at the origin. We prove that $\mathcal{M}_1$ is in one-to-one correspondence with $\mathcal{M}_2\times Z_2$, where…

Interpolates curves using maximal and minimal surfaces in different spaces.

Discrete approximation solves Björling's minimal surface problem.

Paper tackles edge computing for reliable ITS data analytics.

We introduce a class of special geometries associated to the choice of a differential graded algebra contained in ΛR^n. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be realized as submanifolds of a Riemannian manifold with special holonomy, to…

The classical Björling problem is to find the minimal surface containing a given real analytic curve with tangent planes prescribed along the curve. We consider the generalization of this problem to non-minimal constant mean curvature (CMC) surfaces, and show that it can be solved via the loop group formulation for suc…

The paper flattens a non-degenerate CR singular point in complex space.

Survey shows degenerate elliptic equations have analytic properties despite low regularity.

Ancient solutions to heat equations on graphs are shown to be analytic in time.

Stochastic VB improves nonlinear model inference speed and accuracy.

The paper proves real-analyticity of superintegrable metrics and solves two conjectures.

Real analytic submersion images are always real analytic.

This note presents an analytic construction of the optimal unit-norm direction hat(x) = x/|x| that maximizes or minimizes the objective linear expression, B . hat(x), subject to a system of linear constraints of the form [A] . x = 0, where x is an unknown n-dimensional real vector to be determined up to an overall norm…

Ancient solutions of heat equation with exponential growth are analytic in time.

Proves real analyticity on surfaces based on restrictions.

In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donaldson-Thomas equation, to analytically approach the Donaldson-Thomas invariants. In this article, we consider the equation on compact Kähler t…

Neural networks learn modular arithmetic but not all, extending known solutions to generalize.

We begin by showing that every real analytic orbifold has a real analytic Riemannian metric. It follows that every reduced real analytic orbifold can be expressed as a quotient of a real analytic manifold by a real analytic almost free action of a compact Lie group. We then extend a well-known result of Nomizu and Ozek…

We prove each embedded, constant mean curvature (CMC) surface in Euclidean space with genus zero and finitely many coplanar ends is nondegenerate: there is no nontrivial square-integrable solution to the Jacobi equation, the linearization of the CMC condition. This implies that the moduli space of such coplanar surface…

We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known the constructio…

We define a large class of integrable nonlinear PDE's, \emph{$k$-symmetric AKS systems}, whose solutions evolve on finite dimensional subalgebras of loop algebras, and linearize on an associated algebraic curve. We prove that periodicity of the associated algebraic data implies a type of quasiperiodicity for the soluti…

Transforms uniquely determine Higgs fields on real-analytic manifolds.

Proper Lie groupoids have real analytic structures.

We study the problem of the existence and the holomorphicity of the Monge-Ampère foliation associated to a plurisubharmonic solutions of the complex homogeneous Monge-Ampère equation even at points of arbitrary degeneracy. We obtain good results for real analytic unbounded solutions. As a consequence we also provide a …

Wearable tech detects table tennis shots with high accuracy.

Paper constructs counterexamples of higher solutions to self-duality equations.

Study on metrics with singularities on spheres, showing moduli space structure.

In this article, we study an analog of the Björling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $γ$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $γ$, find an isothermic surface that is tangent to $γ$ and that…

Paper presents an analytical solution to Merton Garman model using symmetries.

Paper finds analytical solution for portfolio selection under worst-case model risk.

Paper generalizes a theorem for real analytic singularities.

We construct a smooth Lie group structure on the group of real analytic diffeomorphisms of a compact analytic manifold with corners. This generalises the known analogous results in the situation where the real analytic manifold has no corners. Additionally our approach uses a different construction.

Analytic network learning simplifies multilayer network training without gradients.

We extend the work of Simon and Wickramasekera, who constructed a large class of $C^{1,μ}$ multivalued solutions to the minimal surface equation, to produce $C^{1,μ}$ multivalued solutions to more general classes of elliptic equations and systems, including the minimal surface system with small boundary data and the La…

Paper compares absolute and relative real analytic torsion forms over fibrations.

Analyzing static solutions in Finsler gravity, extending known results.

Smooth rigid spherical hypersurfaces in C^2 are real analytic.

Geometric analysis on real analytic manifolds using seminorms.

Analytical solution found for a three-layer network with a specific activation function.