arXiv research

Study on radial solutions in higher dimensions, finding special cases.

Radial graphs with constant mean curvature found in Euclidean space.

The paper finds hypersurfaces with constant curvature and prescribed boundary in Euclidean space.

We prove that if $M$ is a complete hypersurface in $\mathbb{R}^{n+1}$ which is graph of a real radial function, then the spectrum of the Laplace operator on M is the interval $[0,\infty)$.

Reformulates RBF networks for graph-based data.

We prove the existence and uniqueness of radial graphs over a given domain of $\mathbb{S}^{n}$ having boundary on the sphere $\mathbb{S}^{n}$ and whose mean curvature at every point equals a prescribed positive function satisfying suitable barrier-type and monotonicity conditions.

The paper proves stability of certain graph types in Euclidean space with specific densities.

We show that a smooth radially symmetric solution $u$ to the graphic Willmore surface equation is either a constant or the defining function of a half sphere in ${\mathbb R}^3$. In particular, radially symmetric entire Willmore graphs in ${\mathbb R}^3$ must be flat. When $u$ is a smooth radial solution over a puncture…

Two combinatorial models for moduli space are compared and homotopy equivalence proven.

In this paper we extend a recent result of Collin-Rosenberg ({\it a solution to the minimal surface equation in the Euclidean disc has radial limits almost everywhere}) to a large class of differential operators in Divergence form. Moreover, we construct an example (in the spirit of \cite{CR2}) of a minimal graph in $\…

Modified flow finds constant mean curvature surfaces in hyperbolic space.

Flow preserves area, proving a general isoperimetric inequality.

It is extended a result due to B. Guan and J. Spruck on the asymptotic Plateau's problem for CMC radial graphs in hyperbolic space to horizontal CMC graphs.

First-passage percolation affects graph properties like curvature and geodesics.

In this paper we find strictly locally convex hypersurfaces in $\mathbb{R}^{n+1}$ with prescribed curvature and boundary. The main result is that if the given data admits a strictly locally convex radial graph as a subsolution, we can find a radial graph realizing the prescribed curvature and boundary. As an applicatio…

This paper proves a conjecture linking quantum modular forms and WRT invariants for specific graphs.

We consider the inverse mean curvature flow in smooth Riemannian manifolds of the form $([R_{0},\infty)\times S^n,\bar{g})$ with metric $\bar{g}=dr^2+{\vartheta}^2(r)σ$ and non-positive radial sectional curvature. We prove, that for initial mean-convex graphs over $S^n$ the flow exists for all times and remains a graph…

Method learns graph structure for multi-task learning, revealing interpretable relationships.

Researchers find hypersurfaces in a Riemannian vector bundle with specific curvature.

Existence and uniqueness in ${\Bbb R}^{n,1}$ of entire spacelike hypersurfaces contained in the future of the origin $O$ and asymptotic to the light-cone, with scalar curvature prescribed at their generic point $M$ as a negative function of the unit vector $\overrightarrow{Om}$ pointing in the direction of $\overrighta…

We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan-Hadamard manifold $M$ whose radial sectional curvatures outside a compact set satisfy an upper bound $K(P)\le - \frac{φ(φ-1)}{r(x)^2}$ and a pointwise pinching condition $|K(P)|\le C_K|K(P')|$ for some constants $φ>1$ and $C_K\ge 1…

We extend the interior gradient estimate due to N. Korevaar and L. Simon for solutions of the mean curvature equation from the case of Euclidean graphs to the general case of Killing graphs. Our main application is the proof of existence of Killing graphs with prescribed mean curvature function for continuous boundary …

New proof of self-similar solutions for inverse mean curvature flow.

Study on flat singularities of area-minimizing currents in codimension one.

New matrix approximation method using RBF components for better memory efficiency.

The paper generalizes radial curvature bounds on manifolds.

Study minimal graphs on non-negative Ricci curvature manifolds.

Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a stable inverse map to such a general bi-Lipschitz map. Our approach relies on radial basis functions (RBFs) to interpolate the inverse map ever…

Proof of smooth radial sections in vector bundles.

All radially symmetric connections on round spheres are parallel.

Convexity properties are preserved under radial transformations in hyperbolic and spherical geometries.

Study examines maximal domains of radial harmonic functions across different curvature types.

Study geometry and topology of manifolds with radial curvature bounds.

The study characterizes harmonic spaces and their radial eigen-functions and vector fields.

No radial balanced metrics found on Kepler manifold unit ball with mild boundary conditions.

Study complete gradient Ricci solitons with zero radial Weyl curvature.

New quantum modular forms for specific 3-manifolds discovered.

Radial BNNs offer a scalable, continuous weight distribution for Bayesian deep learning.

Study on surfaces in Heisenberg group with constant mean curvature.

This paper classifies special ends of real projective orbifolds.

New topologies for star-shaped sets without boundedness.

New algorithm radVI improves variational inference by optimizing radial profiles.

New capillary surface found without radial limits at corner.

The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation that the radial flag curvature is bounded below by the radial curvature function of a non-compact surface of revolution, the edge opposite to …

Proves conditions for radial Kaehler metrics to be Kaehler-Einstein.

Study radial processes in sub-Riemannian Brownian motions, proving stochastic completeness and eigenvalue estimates.

Paper finds solutions for convex surfaces in space forms with specific curvature.

Study on gradient ρ-Einstein solitons with radially nonnegative Bach tensor.