Related papers: The Morse-Bott-Kirwan condition is local

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…

This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…

Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum…

We present conditions for reconstruction of Morse-Bott functions with prescribed preimages on $3$-dimensional manifolds. The present work strengthens a previous result for the Morse function case by the author and present a related example…

We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium…

Let $M$ be a proper Hamiltonian $K$-space with proper moment map $\mu$. The symplectic quotient $X=\mu^{-1}(0)/K$ is in general a singular stratified space. In this paper we first generalize the Kirwan map to this symplectic setting which…

Local oscillation of a function satisfying a H\"older condition is considered and it is proved that its growth is governed by a version of the Law of the Iterated Logarithm.

Consider an analytic Hamiltonian system near its analytic invariant torus $\mathcal T_0$ carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at $\mathcal T_0$ is convergent and has a particular form: it is an…

We show that wave maps from Minkowski space $R^{1+n}$ to a sphere are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space $\dot H^{n/2}$ in the high dimensional case $n \geq 5$. A major difficulty,…

Let K be a compact Lie group and fix an invariant inner product on its Lie algebra. Given a Hamiltonian action of K on a compact symplectic manifold X, the normsquare of the moment map defines a Morse stratification of X by locally closed…

We prove that if a continuous piecewise-smooth map on $\mathbb{R}^n$ is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, then it has a fixed point. The result has important…

Using the Girard--Newton formulae, I give a simple proof of isotropic square function estimates for extension operators along the moment curve in generic local fields. Using Bezout's Theorem and the Implicit Function Theorem, I give an…

In this article we prove a generalization of the Beurling--Malliavin Majorant Theorem. In more detail, we establish a new sufficient condition for a function to be a Beurling--Malliavin Majorant. Our result is strictly more general than…

In the local gluing one glues local neighborhoods around the critical point of the stable and unstable manifolds to gradient flow lines defined on a finite time interval $[-T,T]$ for large $T$. If the Riemannian metric around the critical…

It is shown that Schrodinger's equation and Born's rule are sufficient to ensure that the states of macroscopic collective coordinate subsystems are microscopically localized in phase space and that the localized state follows the classical…

We prove the transversality result necessary for defining local Morse chain complexes with finite cyclic group symmetry. Our arguments use special regularized distance functions constructed using classical covering lemmas, and an inductive…

In this paper we are concerned with the global existence of smooth solutions to the turbulent flow equations for compressible flows in $\mathbb{R}^3$. The global well-posedness is proved under the condition that the initial data are close…

We consider the convergence of moving averages in the general setting of ergodic theory or stationary ergodic processes. We characterize when there is universal convergence of moving averages based on complete convergence to zero of the…

The first-order approximation to the solution of the Boltzmann--Curtiss transport equation is derived. The resulting distribution function treats the rotation or gyration of spherical particles as an independent classical variable,…

We investigate global solvability, in the framework of smooth functions and Schwartz distributions, of certain sums of squares of vector fields defined on a product of compact Riemannian manifolds $T \times G$, where $G$ is further assumed…