arXiv research

Proves generic existence of spectral networks for many cases.

The paper examines conditions for Einstein multiply warped products and estimates their parameters.

New bound for neural networks with full-rank weights, independent of network width.

This paper addresses the problem of existence of generalized Landsberg structures on surfaces using the Cartan-Kähler Theorem and a Path Geometry approach.

We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is a…

In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.

The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admits no solution for a broad range of parameters. This suggests that the question of existence or non-existence of solutions to the original e…

Study solves a generalized Christoffel-Minkowski problem using curvature flow.

The present paper deals with the proper existence of a generalized class of recurrent manifolds, namely, hyper-generalized recurrent manifolds. We have established the proper existence of various generalized notions of recurrent manifolds. For this purpose we have presented a metric and computed its curvature propertie…

Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed for this problem that assume a specific click model connecting rankings and user b…

This paper establishes geometric obstructions to the existence of complete, properly embedded, mean curvature flow self-translating solitons $Σ^n\subseteq \mathbb{R}^{n+1}$, generalizing previously known non-existence conditions such as cylindrical boundedness.

We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.

Existence of minimizers proven for residual ANNs with ReLU activation.

Solves a generalized dual Minkowski problem for specific values of q.

Proves existence of circle patterns on surfaces with cusps.

Introduces generalized Yamabe flows with long-time existence and convergence results.

Paper explores existence and nonexistence of submanifolds in contact geometry.

The paper examines Nash equilibrium in GANs for stationary Gaussian processes.

The $(α,β)$-Ricci-Yamabe flow exists on closed manifolds.

Proves existence and uniqueness of loop equation solutions for semisimple Frobenius manifolds.

The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The existence of bundle coordinates normal at a given point and/or along injective horizonta…

Conformally equivariant quantization is a peculiar map between symbols of real weight $δ$ and differential operators acting on tensor densities, whose real weights are designed by $λ$ and $λ+δ$. The existence and uniqueness of such a map has been proved by Duval, Lecomte and Ovsienko for a generic weight $δ$. Later, Si…

In this paper, we consider the generalized lambda constant and the existence of ground states of the generalized Perelman's W-functional from a variational formulation. One result is concerned with the estimation of the generalized $λ$ constant. The other results are about the existence of ground states of generalized …

This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and an integer-valued random measure, generalizing existing approaches in the litera…

Study proves higher-order conformal forms don't exist in odd dimensions.

In this work, we obtain a existence criteria for the longtime Kähler Ricci flow solution. Using the existence result, we generalize a result by Wu-Yau on the existence of Kähler Einstein metric to the case with possibly unbounded curvature. Moreover, the Kähler Einstein metric with negative scalar curvture must be uniq…

Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven fashion, (twisted) generalized complex structures are constructed on a myriad of four-…

Paper proves regularity and existence of Riemannian splines.

TOMA generates abstract graphs for RL, reducing memory and computation costs.

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.

In [5], Sáez and Schnürer studied the graphical mean curvature flow of complete hypersurfaces defined on subsets of Euclidean space. They obtained long time existence. Moreover, they provided a new interpretation of weak mean curvature flow. In this paper, we generalize their results to a general curvature setting. Our…

We provide a complete study of existence and uniqueness of solutions to the Lichnerowicz equation in general relativity with arbitrary mean curvature.

We establish short-time existence and regularity for higher-order flows generated by a class of polynomial natural tensors that, after an adjustment by the Lie derivative of the metric with respect to a suitable vector field, have strongly parabolic linearizations. We apply this theorem to flows by powers of the Laplac…

Proves existence of longest paths in sub-Lorentzian problems.

Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.

The Skew Mean Curvature Flow(SMCF) is a Schrödinger-type geometric flow canonically defined on a co-dimension two submanifold, which generalizes the famous vortex filament equation in fluid dynamics. In this paper, we prove the local existence and uniqueness of general dimensional SMCF in Euclidean spaces.

We study the steady state solutions of a generalized logistic type equation on a complete Riemannian manifold. We provide sufficient conditions for existence, respectively non-existence of positive solutions, which depend on the relative size of the coefficients and their mutual interaction with the geometry of the man…

In this paper, we prove an existence theorem of a local moduli space for geometric structures in a very general setting. Then to show the interest of this result, we apply it to the case of sasakian and Sasaki-Einstein structures.

DG algorithms often fail to generalize well in limited domains, highlighting necessary vs. sufficient conditions.

Sharpness minimization algorithms don't solely improve generalization.

Convex curves evolve into circles over time.

Paper shows equivalence between NA and ACLMM in diffusion models.

Paper tightens CMI bounds for learning algorithms.

The objective of this paper is to introduce the notion of generalized almost statistical (briefly, GAS) convergence of bounded real sequences, which generalizes the notion of almost convergence as well as statistical convergence of bounded real sequences. As a special kind of Banach limit functional, we also introduce …

We show that there exists an interval exchange and a point so that the orbit of the point equidistributes for a measure that is not ergodic.

Generalizes existence of bending laminations for Kleinian groups.

KSGAN uses KS distance for deep generative modeling.

In this paper, we generalize our apriori estimates on cscK(constant scalar curvature Kähler) metric equation to more general scalar curvature type equations (e.g., twisted cscK metric equation). As applications, under the assumption that the automorphism group is discrete, we prove the celebrated Donaldson's conjecture…