arXiv research

Method uses DNNs to approximate functions with specific asymptotic behavior.

Study asymptotic behaviors of solutions near singular boundaries for the Yamabe problem.

The paper analyzes the asymptotic behavior of a knot polynomial for a specific real number.

In this paper we investigate the asymptotic behavior of the colored HOMFLY polynomial of the figure eight knot associated with the symmetric representation. We establish an analogous asymptotic expansion for the colored HOMFLY polynomial. From the asymptotic behavior we show that the Chern-Simons invariants and twisted…

Study on manifolds with kinks and Gaussian kernel behavior.

Study on steady solitons' curvature behavior near infinity.

Study asymptotic behavior of Weingarten surfaces at infinity.

Wide networks with polynomial activations have proven asymptotic behavior.

We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.

Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the l…

Study Goeritz groups of link decompositions, focusing on their asymptotic behavior.

Study of Moncrief lines' behavior in curved space-times.

In this paper we give new existence results for complete non-orientable minimal surfaces in $\mathbb{R}^3$ with prescribed topology and asymptotic behavior.

We use a method, inspired by Pohozeav's work, to study asymptotic behaviors of non-variational elliptic systems in dimension n greater than two. The results apply to changing sign solutions.

New filling functions for groups with coefficients show different asymptotic behavior.

In this paper we prove a universal inequality describing the asymptotic behavior of support points for planar continuous curves. As corollaries we get an analogous result for tangent points of differentiable planar curves and some (partially known) assertions on the asymptotic of the mean value points for various class…

In this paper, we analyze the asymptotic behavior of $κ$-noncollapsed and positively curved steady Ricci solitons and prove that any $n$-dimensional $κ$-noncollapsed steady Kähler-Ricci soliton with non-negative sectional curvature must be flat.

Study on asymptotic behavior of Taub-NUT type solitons and construction of new ALF Calabi-Yau metrics.

Study confirms asymptotic behavior of logarithmic balanced metric near infinity.

The paper studies the asymptotic behavior of adversarial training under $\ell_\infty$-perturbation.

Study geodesics in conformally compact manifolds, showing smoothness and asymptotic behavior.

In this paper, we introduce a monotonicity formula for the mean curvature flow which is related to self-expanders. Then we use the monotonicity to study the asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces.

The metric is quite singular at infinity and it is not complete. Using these expansions, we have a more precise description of the asymptotic behavior of quasi-harmonic functions and of eigenfunctions of drift-Laplacian at infinity.

Study on high-codimensional minimal surfaces in hyperbolic space.

We clarify and refine the relation between the asymptotic behavior of the colored Jones polynomial and Chern-Simons gauge theory with complex gauge group SL(2,C). The precise comparison requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of pola…

We study the short-time asymptotics of conditional expectations of smooth and non-smooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the semimartingale. We derive in particular the asymptotic behavior of call options with sho…

In this paper, we study the exterior problem for the maximal surface equation. We obtain the precise asymptotic behavior of the exterior solution at infinity. And we prove that the exterior Dirichlet problem is uniquely solvable given admissible boundary data and prescribed asymptotic behavior at infinity.

Study on Einstein solitons with bounds and asymptotic behavior.

Constant mean curvature (CMC) surfaces in space forms can be described by their associated $\mathbb C^*$-family of flat $SL(2,\mathbb C)$-connections $\nabla^λ$. In this paper we consider the asymptotic behavior (for $λ\to0$) of the gauge equivalence classes of $\nabla^λ$ for compact CMC surfaces of genus $g\geq2.$ We …

In this paper, we study the existence, uniqueness and asymptotic behavior of rotationally symmetric translating solitons of the mean curvature flow in Minkowski space. We also study the asymptotic behavior and the strict convexity of general solitons of such flows.

In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kahler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct a explicit sequence of Kahler metrics with special approximating properties. Using those metrics as s…

The paper studies the curvature behavior near the boundary of certain domains.

We compute the Hessian of quantized Ding functionals and give an elementary proof for the convexity of quantized Ding functionals along Bergman geodesics from the view point of projective geometry. We study also the asymptotic behavior of the Hessian using the Berezin-Toeplitz quantization.

The paper studies the asymptotic behavior of HCMA equations on ALE Kahler manifolds.

The paper studies heat behavior on curved spaces without radiality assumption.

Study shows quantum behavior near infinity in metric asymptotics.

Study low energy resolvent behavior on fibred boundary metrics.

The study examines the asymptotic behavior of extremal length in Teichmüller space.

The paper defines a new condition for Fano manifolds and shows its implications on their asymptotic behavior.

We determine the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a Robertson-Walker space-time. We prove in particular that when approaching the explosion time of the diffusion, its projection on the base manifold almost surely converges to a random point of the …

Study of Dirichlet minimizers on manifolds with boundary and their asymptotic behavior.

The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and Lojasiewicz inequality), tight bounds on the asymptotic bias of the iterates generated b…

Constructs self-expanders of positive genus for cones in R^3.

We describe the asymptotic behavior of Palais-Smale sequences associated to certain Yamabe-type equations on manifolds with boundary. We prove that each of those sequences converges to a solution of the limit equation plus a finite number of "bubbles" which are obtained by rescaling fundamental solutions of the corresp…

For a hyperbolic knot and a natural number n, we consider the Alexander polynomial twisted by the n-th symmetric power of a lift of the holonomy. We establish the asymptotic behavior of these twisted Alexander polynomials evaluated at unit complex numbers, yielding the volume of the knot exterior. More generally, we pr…

We consider the asymptotic behavior of properly embedded minimal surfaces in the product of the hyperbolic plane with the line, taking into account the fact that there is more than one natural compactification of this space. This provides a better setting in which to consider the general problem of determining which cu…

We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak …

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model…