相关论文: Morse functions statistics

We give an exposition of the Morse Index Theorem in the Riemannian case in terms of the Maslov index, following and expanding upon Arnold's seminal paper. We emphasize the symplectic arguments in the proof and aim to be as self-contained as…

The hemisphere soft function is calculated to order alpha_s^2. This is the first multi-scale soft function calculated to two loops. The renormalization scale dependence of the result agrees exactly with the prediction from effective field…

The minimal possible rate of growth of a meromorphic function with three critical values is found.

In this paper, we study the computation of optimal discrete Morse functions on stratifolds. In particular, we present an algorithm that efficiently computes such functions for a broad class of them. Moreover, we characterize the conditions…

For an open manifold $M$ and a function $v$ with bounded growth of derivative, there exists a Riemannian metric of bounded geometry on $M$ such that the volume growth function lies in the same growth class as $v$. This was proved by R.…

Morse functions are important objects and tools in understanding topologies of manifolds since the 20th century. Their classification has been natural and difficult problems, and surprisingly, this is recently developing. Since the 2010's,…

We examine the measurable chromatic number of distance colorings on the surface of 2-dimensional spheres of varying radii, showing in particular that similar arguments to those used to raise lower bounds in the plane work for all but a…

This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…

This note establishes several integral identities relating certain metric properties of level hypersurfaces of Morse functions.

In some of his final papers, V.I. Arnold studied pseudorandomness properties of finite deterministic sequences, which he measured in terms of their "stochasticity parameter". In the present paper we illustrate the background in probability…

In this paper, the theory of functions of one complex variable is explored to study linearly full unramified holomorphic two-spheres with constant curvature in $G(2,n)$ satisfying that the generated harmonic sequence degenerates at position…

This is the second in a two part series of papers concerning Morse quasiflats - higher dimensional analogs of Morse quasigeodesics. Our focus here is on their asymptotic structure. In metric spaces with convex geodesic bicombings, we prove…

BMO estimates and the radial growth of Bloch functions have been studied by B. Korenblum [3]. The present paper contains some natural generalizations of these results.

We discuss meromorphic functions on the complex plane which are Brody curves regarded as holomorphic maps to P_1, i.e., which have bounded spherical derivative.

In our present investigation we propose to study and develop the I-function of two variables analogous to the I-function of one variable introduced and studied by one of the authors[24]. The conditions for convergence, series…

The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra.…

In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.

Estimates of some integrals related to variations of smooth functions are presented.

In this note, we solve the Gauss image problem given two Borel measures on the unit sphere, one of which is absolutely continuous with respect to the uniform measure.

In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general class of metric measure spaces. We then…