arXiv research

Algorithm finds minimal standardizer of parabolic subgroups in Artin-Tits groups.

Study minimal networks on spheres and balls near standard metrics.

Simplifies risk minimization combining mean and standard deviation.

In 1993, Y.-G. Oh proposed a problem whether standard Lagrangian tori in C^n are volume minimizing under Hamiltonian isotopies of C^n. In this article, we prove that most of them do not have such property if the dimension n is greater than two. We also discuss the existence of Hamiltonian non-volume minimizing Lagrangi…

Optimizes sharp curvature inequality on spheres, proving near-minimizers are close to standard metric.

This work proposes SDI regularization to improve adversarial robustness.

We describe a 3-parametric family $\mathcal{K}$ of properly embedded minimal tori with four parallel ends in quotients of $\mathbb{R}^3$ by two independent translations, which we will call the \textit{Standard Examples.} These surfaces generalize the examples given by Karcher, Meeks and Rosenberg in \cite{ka4,ka6,mr3}.…

It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three dimensional Riemannian Heisenberg group. It is also shown that they are the only surfaces in the three dimensional Heisenberg group whose mean curvature is zero with respect to both of th…

Standard embeddings of Schubert varieties in specific manifolds characterized.

We propose a method for building an interpretable recommender system for personalizing online content and promotions. Historical data available for the system consists of customer features, provided content (promotions), and user responses. Unlike in a standard multi-class classification setting, misclassification cost…

The study finds counterexamples to curvature estimates for minimizing surfaces.

Soft cells fill space without gaps, derived from minimal surfaces and deformed using edge bending.

Standard cohomology of Courant algebroids identified via minimal models.

Minimal crystallizations of simply connected PL 4-manifolds are very natural objects. Many of their topological features are reflected in their combinatorial structure which, in addition, is preserved under the connected sum operation. We present a minimal crystallization of the standard PL K3 surface. In combination w…

We present conditions on the Ricci curvature for complete, oriented, minimal submanifolds of Euclidean space, as well as the standard unit sphere, when the Gauss maps are bounded embeddings.

Study finds minimal coloring numbers for torus links using rack colorings.

New method outperforms standard procedures in heavy-tailed problems.

Efficiently minimizes regret in non-convex games with gradient-based methods.

In this note, we investigate the well-known Yau rigidity theorem for minimal submanifolds in spheres. Using the parameter method of Yau and the DDVV inequality verified by Lu, Ge and Tang, we prove that if $M$ is an $n$-dimensional oriented compact minimal submanifold in the unit sphere $S^{n+p}(1)$, and if $K_{M}\geq\…

New minimal link diagrams found, including torus links and homogeneous ones.

Freedman, He, and Wang, conjectured in 1994 that the Mobius energy should be minimized, among the class of all nontrivial links in Euclidean space, by the stereographic projection of the standard Hopf link. We prove this conjecture using the min-max theory of minimal surfaces.

We present a conjecture, based on computational results, on the area minimizing way to enclose and separate two arbitrary volumes in the flat cubic 3-torus. For comparable small volumes, we prove that an area minimizing double bubble in the 3-torus is the standard double bubble from R^3.

New algorithm SELECT minimizes satisficing regret in bandits.

All principal orbits of the standard Hamiltonian $T^n$-action on the complex projective space ${\mathbb C}P^n$ are Lagrangian tori.In this article, we prove that most of them are not volume minimizing under Hamiltonian isotopies of ${\mathbb C}P^n$ if the complex dimension $n$ is greater than two, although they are Ham…

We show that the standard minimal genus Heegaard splitting of (closed orientable surface)\times S^1 is a critical Heegaard splitting.

Study on high-codimensional minimal surfaces in hyperbolic space.

New proof of a unique 3-part partition in 8D space.

Hexagonal tilings minimize perimeter with unequal volumes.

We consider the minimal entropy problem, namely the question of whether there exists a smooth metric of minimal entropy, for certain classes of 3-manifolds. Among other resulsts, we show that if M is a closed, orientable, geometrizable 3-manifold with zero simplicial volume, then the minimal entropy can be solved for M…

Proves Miyaoka-Yau inequality for minimal pairs using Kähler-Einstein metrics.

A new method for 1-bit matrix completion that is faster and more accurate.

Solves empirical risk minimization for relational data using graph sampling.

We investigate the minimal surface problem in the three dimensional Heisenberg group, H, equipped with its standard Carnot-Caratheodory metric. Using a particular surface measure, we characterize minimal surfaces in terms of a sub-elliptic partial differential equation and prove an existence result for the Plateau prob…

Let $M$ be a Riemannian 3-manifold of nonnegative Ricci curvature, Ric $\geq 0.$ We suppose that $M$ is conformally flat and simply connected or more generally that it admits a conformal immersion into the standard 3-sphere. Let $Σ$ be a compact connected and orientable surface immersed in $M$ which is a stable constan…

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature to a metric conformal to the standard one. Our proof involves the study of crit…

A left invariant metric on a nilpotent Lie group is called minimal, if it minimizes the norm of the Ricci tensor among all left invariant metrics with the same scalar curvature. Such metrics are unique up to isometry and scaling and the groups admitting a minimal metric are precisely the nilradicals of (standard) Einst…

The paper constructs stable minimal hypersurfaces with specific singularities.

This study connects Jacobian regularization to adversarial robustness and improves generalization.

JTT improves model worst-group accuracy without group annotations.

We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the standard methods for minimizing the usual notion of regret fail, through our analysis …

Let $D_n$ denote the $n$-punctured disk in the complex plane, where the punctures are on the real axis. An $n$-braid $α$ is said to be \emph{reducible} if there exists an essential curve system $\C$ in $D_n$, called a \emph{reduction system} of $α$, such that $α*\C=\C$ where $α*\C$ denotes the action of the braid $α$ o…

The study of stable and index compact minimal submanifolds in Berger spheres.

Unified algorithm for minimizing composite functions with flexible design.

IRM fails to improve over standard methods in complex settings.

Efficiently constructs prediction bands with minimal assumptions.

This paper shows how to learn variational inequalities fast with strong monotonicity.

Extends fair empirical risk minimization to continuous sensitive attributes.

New algorithm minimizes worst-case regret in uncertain, time-varying dynamics.