arXiv research

Study on stable minimal hypersurfaces under Ricci curvature constraints.

Method decomposes streaming data into sparse and low-rank components from compressive measurements.

The paper proves a Wulff inequality for minimal submanifolds with boundary in Euclidean space.

The paper proves weighted monotonicity theorems in various spaces and applies them to minimal surfaces.

The paper proves an infinite double bubble theorem in higher dimensions.

We study stability properties of $f$-minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-Emery Ricci curvature under volume growth conditions. Moreover, exploiting a weighted version of a finiteness result and the adaptation to this setting of Li-Tam theory, we investigate the top…

A framework learns graph structure from smooth signals using weighted ℓ-1 minimization.

In this paper, we investigate minimizing properties of the map $x/\|x\|$ from the Euclidean unit ball $\mathbf{B}^{n}$ to its boundary $\mathbb{S}^{n-1}$, for the weighted energy functionals $E^n\_{p,α}(u)=\int\_{\mathbf{B}^{n}} \|x\|^α\|\nabla u\|^p dx$. We establish the following induction principle: if the map $\fra…

The paper proposes a method to solve L1 regression with fewer labels using Lewis weights.

The paper proves smoothness of almost-minimizers' boundaries near the free boundary.

Study on the index and Betti number of f-minimal hypersurfaces and self-shrinkers.

Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.

In this paper, we investigate the minimality of the map $\frac{x}{\|x\|}$ from the euclidean unit ball $\mathbf{B}^n$ to its boundary $\mathbb{S}^{n-1}$ for weighted energy functionals of the type $E\_{p,f}= \int\_{\mathbf{B}^n}f(r)\|\nabla u\|^p dx$, where $f$ is a non-negative function. We prove that in each of the t…

In this paper, we obtain results on rigidity of complete Riemannian manifolds with weighted Poincaré inequality. As an application, we prove that if $M$ is a complete $\frac{n-2}{n}$-stable minimal hypersurface in $\mathbb{R}^{n+1}$ with $n\geq 3$ and has bounded norm of the second fundamental form, then $M$ must eithe…

Optimizes matching in weighted graphs with semi-bandit sampling.

Study on isoperimetric inequality on weighted Riemannian manifolds with negative effective dimension.

The paper studies stability and minimizing properties of higher codimensional surfaces in Euclidean space.

New minimal hypersurfaces in 4D sphere found.

Paper proves a sharp weighted Isoperimetric inequality for substatic manifolds.

We derive the Simons' type equation for $f$-minimal hypersurfaces in weighted Riemannian manifolds and apply it to obtain a pinching theorem for closed $f$-minimal hypersurfaces immersed in the product manifold $\mathbb{S}^n(\sqrt{2(n-1)})\times \mathbb{R}$ with $f=\frac {t^2}{4}$. Also we classify closed $f$-minimal h…

We prove overfitting in minimal and random NNs, tempering the effect.

The paper proves cohomology vanishing for a specific type of minimal submanifolds in a weighted Euclidean ball.

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their correspondi…

BiTAT improves neural network quantization for edge devices by focusing on weight dependencies and disentangling them.

Let $Ω$ be an open half-space or slab in $\mathbb{R}^{n+1}$ endowed with a perturbation of the Gaussian measure of the form $f(p):=\exp(ω(p)-c|p|^2)$, where $c>0$ and $ω$ is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to $\partialΩ$. In this work we follow a varia…

The paper extends Hamiltonian stability and mean curvature flow to Fano manifolds.

New weight systems derived from a specific Lie algebra for knot invariants.

The paper proves strict convexity of the Mabuchi functional for geodesics connecting energy minimizers.

Study on Gauss images of specific minimal surfaces with finite curvature.

Optimal Euclidean structure minimizes energy in weighted toroidal graphs.

Paper addresses regret minimization and inference in high-dimensional online decision-making.

Corrects sample selection bias in empirical risk minimization using importance sampling.

Study proves no minimal surfaces can be contained in certain half-spaces or cones.

Hyperplanes, hyperspheres and hypercylinders in $\Bbb R^n$ with suitable densities are proved to be weighted minimizing by a calibration argument. Also calibration method is used to prove a weighted minimal hypersurface is weighted area-minimizing locally.

Study on optimal ReLU networks with weight decay for interpolation.

Minimal surface equation results in constant solutions on RCD spaces.

We have introduced the weight of a group which has a presentation with number of relations is at most the number of generators. We have shown that the number of facets of any contracted pseudotriangulation of a connected closed 3-manifold $M$ is at least the weight of $π(M, \ast)$. This lower bound is sharp for the 3-m…

Fewer data weight updates lead to faster convergence in machine learning models.

Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear norm minimization will exactly recover the low rank matrix. In this article, we…

New algorithm trains ReLU networks via alternating minimization.

Let $(M^{n+1},g,e^{-f}dμ)$ be a complete smooth metric measure space with $2\leq n\leq 6$ and Bakry-Émery Ricci curvature bounded below by a positive constant. We prove a smooth compactness theorem for the space of complete embedded $f$-minimal hypersurfaces in $M$ with uniform upper bounds on $f$-index and weighted vo…

Paper resolves Chern conjecture for 4D minimal hypersurfaces in S5.

Researchers find continuous solutions to minimizers in weighted least gradient problems.

New method speeds up subspace clustering by 20-30x.

Paper provides recovery guarantees for weighted low-rank approximation via alternating minimization.

The paper analyzes prediction error in nonstationary settings using weighted risk minimization.

Ridgeless ReLU networks interpolate datasets and extrapolate based on curvature signs.

The study connects minimal and maximal surfaces in 3D and 3-L space.