arXiv research

The study shows ends of shrinking gradient $ρ$-Einstein solitons are non-parabolic.

Let $M^m$, with $m\geq 3$, be an $m$-dimensional complete noncompact manifold isometrically immersed in a Hadamard manifold $\bar M$. Assume that the mean curvature vector has finite $L^p$-norm, for some $2\leq p\leq m$. We prove that each end of $M$ must either have finite volume or be non-parabolic.

Study of ends of complete gradient Schouten solitons, showing finitely many ends for shrinking and connected infinity for expanding ones.

Defines non-parabolic curves in spatial hybrid space with applications.

Finite graphs with specific curvature have limited harmonic functions and ends.

In this paper we consider the conformal type (parabolicity or non-parabolicity) of complete ends of revolution immersed in simply connected space forms of constant sectional curvature. We show that any complete end of revolution in the $3$-dimensional Euclidean space or in the $3$-dimensional sphere is parabolic. In th…

We give a topological interpretation of the space of $L^2$-harmonic forms on Manifold with flat ends. It is an answer to an old question of J. Dodziuk. We also give a Chern-Gauss-Bonnet formula for the $L^2$-Euler characteristic of some of these Manifolds. These results are applications of general theorems on complete …

$Sol_3$ is shown not to be parabolic.

Using the monotonicity formulas of Colding and Minicozzi, we prove that on any complete, non-parabolic Riemannian manifold $(M^3, g)$ with non-negative Ricci curvature, the asymptotic weighted scaling invariant integral of scalar curvature has an explicit bound in form of asymptotic volume ratio.

Sharp gradient estimate for Green functions on non-parabolic RCD(0,N) spaces.

In this paper we show that the existence of a non-parabolic local cut point in the Bowditch boundary $\partial(G,\mathbb{P})$ of a relatively hyperbolic group $(G,\mathbb{P})$ implies that $G$ splits over a $2$-ended subgroup. This theorem generalizes a theorem of Bowditch from the setting of hyperbolic groups to relat…

Cuspidal edges and swallowtails are typical non-degenerate singular points on wave fronts in the Euclidean $3$-space. Their first fundamental forms belong to a class of positive semi-definite metrics called "Kossowski metrics". A point where a Kossowski metric is not positive definite is called a singular point or a se…

We extend classical Euclidean stability theorems corresponding to the nonrelativistic Hamiltonians of ions with one electron to the setting of non parabolic Riemannian 3-manifolds.

We study Kahler manifolds-with-boundary, not necessarily compact, with weakly pseudoconvex boundary, each component of which is compact. If such a manifold $K$ has $l\ge2$ boundary components (possibly $l=\infty$), then it has first betti number at least $l-1$, and the Levi form of any boundary component is zero. If $K…

Let $M$ be a complete non-compact manifold satisfying the volume doubling condition, with doubling index $N$ and reverse doubling index $n$, $n\le N$, both for large balls. Assume a Gaussian upper bound for the heat kernel, and an $L^2$-Poincaré inequality outside a compact set. If $2<n$, then we show that for $p\in (2…

We prove an existence result for the Poisson equation on non-compact Riemannian manifolds satisfying weighted Poincaré inequalities outside compact sets. Our result applies to a large class of manifolds including, for instance, all non-parabolic manifolds with minimal positive Green's function vanishing at infinity. On…

The study finds a lower bound for the diameter of gradient ρ-Einstein solitons.

Consider a three dimensional cusped spherical $\mathrm{CR}$ manifold $M$ and suppose that the holonomy representation of $π_1(M)$ can be deformed in such a way that the peripheral holonomy is generated by a non-parabolic element. We prove that, in this case, there is a spherical $\mathrm{CR}$ structure on some Dehn sur…

We construct a parabolic entire minimal graph $S$ over a finite topology complete Riemannian surface $Σ$ of curvature $-1$ and infinite area (thus of non-parabolic conformal type). The vertical projection of this graph yields a harmonic diffeomorphism from $S$ onto $Σ$. The proof uses the theory of divergence lines to …

Simple proof that stable minimal hypersurfaces in R^4 are hyperplanes.

A primary goal in this paper is to study the question that asks when a real analytic submanifold $M$ in ${\mathbb{C}}^{n+1}$ bounds a real analytic (up to $M$) Levi-flat hypersurface $\hat{M}$ near $p\in M$ such that $\hat{M}$ is foliated by a family of complex hypersurfaces moving along the normal direction of $M$ at …

We consider non-elementary representations of two generator free groups in $PSL(2,\mathbb{C})$, not necessarily discrete or free, $G = < A, B >$. A word in $A$ and $B$, $W(A,B)$, is a palindrome if it reads the same forwards and backwards. A word in a free group is {\sl primitive} if it is part of a minimal generating …

The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding the $L^2$-Wasserstein distance of optimal mass transport, and the Fisher--Rao me…

Ends and cohomology theory for noncompact spaces.

End-to-end portfolio system accounts for model risk.

Regularization is important for end-to-end speech models, since the models are highly flexible and easy to overfit. Data augmentation and dropout has been important for improving end-to-end models in other domains. However, they are relatively under explored for end-to-end speech models. Therefore, we investigate the e…

Develops Bayesian approach for end-to-end learning in stochastic optimization.

Study shows mapping class groups are one-ended for surfaces with at least one end.

We give a mathematical foundation for, and numerical demonstration of, the existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1 surface is an ``elliptic end'' (resp. a ``hyperbolic end'') if the monodromy matrix at the …

End-to-end speech recognition system trained on GPUs and CPUs.

End-to-end autonomous driving models get better uncertainty estimates.

This work proposes splitting deep neural networks into smaller sub-networks for faster and more efficient distillation.

End-to-end learning refers to training a possibly complex learning system by applying gradient-based learning to the system as a whole. End-to-end learning system is specifically designed so that all modules are differentiable. In effect, not only a central learning machine, but also all "peripheral" modules like repre…

End-to-end autonomous driving perception learns latent features for better performance.

Study end sum for surfaces and prove uniqueness results.

Study of non-metrizable manifolds' ends, generalizing Nyikos's theorem.

Paper constructs a minimal surface with specific ends and curvature.

Kauri is a novel unsupervised binary tree for clustering that outperforms existing methods.

Researchers found multiple ways to end-sum 4-manifolds, contradicting a previous conjecture.

End-to-end solution for recognizing handwritten numerals, avoiding traditional preprocessing steps.

New Hilbert bundles with ends defined from indexed bases.

Estimates ends of Ricci shrinkers, focusing on smooth and singular cases.

End-to-end policy learning improves statistical arbitrage trading.

End-to-end audio recognition system improves accuracy.

Derives an index formula for families of end-periodic Dirac operators.

End-to-end text-to-speech (TTS) synthesis is a method that directly converts input text to output acoustic features using a single network. A recent advance of end-to-end TTS is due to a key technique called attention mechanisms, and all successful methods proposed so far have been based on soft attention mechanisms. H…

New maxfaces with Enneper ends found.

The study counts ends on shrinkers using geometric covering methods.