arXiv research

A new geometric flow $K$-flow on 3-manifolds shrinks or preserves homogeneous spheres.

We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extendin…

In this work we address the problem of argument search. The purpose of argument search is the distillation of pro and contra arguments for requested topics from large text corpora. In previous works, the usual approach is to use a standard search engine to extract text parts which are relevant to the given topic and su…

This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta pricing relation in place of the market. Thus the difference between the arbitrag…

Study geometric flows of G2-structures, determining curvature and torsion invariants.

With the advancement in argument detection, we suggest to pay more attention to the challenging task of identifying the more convincing arguments. Machines capable of responding and interacting with humans in helpful ways have become ubiquitous. We now expect them to discuss with us the more delicate questions in our w…

Simplified argument for second order estimate in quaternionic Calabi-Yau problem.

This is a continuation of our first paper in [WY16]. There are two purposes of this paper: One is to give a proof of the main result in [WY16] without going through the argument depending on numerical effectiveness. The other one is to provide a proof of our conjecture, mentioned in [TY], where the assumption of negati…

For $J$-holomorphic mappings for a strongly pseudo-convex manifold, we prove elliptic regularity by the argument of boots-strapping.

SpArX creates faithful explanations of neural networks' decision-making.

Killing fields on compact pseudo-Kähler manifolds are holomorphic.

In this article I describe my recent geometric localization argument dealing with actions of NONcompact groups which provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed in [Sch]. A corresponding problem in the compact group setting was so…

Study extends Elkalla's work on subnormal subgroups to $PD_3$-groups, but $L^2$-Betti numbers need verification.

Study improves curvature estimate for stable marginally outer trapped hypersurfaces with a free boundary.

Simplified Obata-Vétois argument for Einstein manifolds with nonnegative scalar curvature.

New argument suggests torsion cannot be part of gravity models.

The paper simplifies arguments for stationary varifolds results.

The paper develops axioms for uniquely decomposing functions with real arguments.

Paper uses ML to predict utility in APS dialogue outcomes.

A new method extracts events and their arguments efficiently from text.

Complete Calabi-Yau metrics made on special 3D spaces.

New argument for 3-manifold cohomology with $\mathbb{F}_2$ coefficients.

This note presents the handlebody argument for modifying achiral Lefschetz singularities into broken Lefschetz fibrations, yielding a handlebody proof of the existence of broken Lefschetz fibrations on arbitrary closed smooth oriented 4-manifolds based on the earlier work of Gay and Kirby. Appeared in Geometry and Topo…

We equip many non compact non simply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly non generic property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new result…

Extends arguments to limit structure in Calabi-Yau degenerations.

We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error f…

We propose a novel method for fact-checking on knowledge graphs based on debate dynamics. The underlying idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to justify the fact being true (…

Causal discovery algorithms can help generate legal arguments.

We propose a novel method for automatic reasoning on knowledge graphs based on debate dynamics. The main idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to promote the fact being true (…

Study restricts line arrangements with odd points using topological arguments.

We consider the classical "Serrin symmetry result" for the overdetermined boundary value problem related to the equation $Δu=-1$ in a model manifold of non-negative Ricci curvature. Using an extension of the Weinberger classical argument we prove a Euclidean symmetry result under a suitable "compatibility" assumption b…

We prove the smoothness of the L^2-analytic torsion form on some fiber bundles with non-compact fibers of positive Novikov-Shubin invariant. We do so by generalizing the arguments of Azzali-Goette-Schick to an appropriate Sobolev space, and proving that the Novikov-Shubin invariant remains positive in the Sobolev setti…

Derives Lagrangian for minimal surfaces, proving tangential variations vanish.

In the present paper, we discuss contra-arguments concerning the use of Pareto-Levý distributions for modeling in Finance. It appears that such probability laws do not provide sufficient number of outliers observed in real data. Connection with the classical limit theorem for heavy-tailed distributions with such type o…

The study examines the long-term behavior of mean curvature flows in closed 3-manifolds.

Direct proof shows adaptive gradient descent converges near-linearly for convex functions.

It is argued that arguments for strict prohibition of interests must be based on the use of arguments from authority. This is carried out by first making a survey of so-called dialectical roots for interest prohibition and then demonstrating that for at least one important positive interest bearing financial product, t…

It has been pointed out to the author by David Glickenstein that the proof of the (closely related) Lemmas 1.2 and 3.2 in the title paper is incorrect. The statements of both Lemmas are correct, and the purpose of this note is to give a correct argument. The argument is of some interest in its own right.

Study solves complex equation on specific types of manifolds.

Proves quantitative Alexandrov theorem for capillary surfaces.

Explain Arnold's proof of the Morse index theorem using Maslov index.

Paper provides a formula for translating solitons and singular minimal surfaces.

We give a new proof of the fact that the condition of a Fano manifold admitting a Kähler-Einstein metric is Zariski-open (provided that the automorphism group is discrete). This proof does not use the characterisation involving stability. The arguments involve estimates of Futaki invariants obtained from a differential…

Recently Dicks-Linnell determined the $L^2$-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator gr…

Classifies metrics with specific curvature properties on a ball.

Paper confirms Whitehead's conjecture for aspherical 2-complexes.

Solves the Merton investment-consumption problem using a new approach.

We prove that every entire self-shrinking solution on $\mathbb{C}^n$ to the Kähler-Ricci flow with strictly real convex potential must be quadratic. The very same argument also gives a pointwise proof for the rigidity of entire self-shrinking solutions to Lagrangian mean curvature flow in pseudo-Euclidean space obtaine…