1 Contents Applications of Hamilton's Compactness Theorem for Ricci flow Peter Topping 1 Applications of Hamilton's Compactness Theorem for Ricci flow 3 Overview 3 Background reading 4 Lecture 1. Ricci flow basics – existence and singularities 5 1.1. Initial PDE remarks 5 1.2. Basic Ricci flow theory 6 Lecture 2. Cheeger-Gromov convergence and Hamilton's compactness theorem 9 2.1. Convergence a...

We establish the global lower mass-bound property for largest connected components in critical window configuration model when degree distribution has an infinite third moment. The scaling limit of percolation clusters, viewed as measured metric spaces, was established our prior work with respect to Gromov-weak topology. Our result extends those results stronger Gromov-Hausdorff-Prokhorov topol...

Abstract We prove the existence of infinitely many time-periodic solutions nonlinear Schrödinger equations using pseudo-holomorphic curve methods from Hamiltonian Floer theory. For generalization Gromov–Floer compactness theorem to infinite dimensions, we show how solve arising small divisor problem by combining elliptic with results theory diophantine approximations.

The abstract model-theoretic concepts of compactness and Löwenheim–Skolem properties are investigated in the “softer” framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institutio...

dL(Mo,M1) = inf[llogdil/l + Ilogdil/-II], f where I: Mo -+ MI is a homeomorphism and dil I is the dilatation of I given by dill = SUPXt#2 dist(f(x l ), l(x2))/ dist(x1 ,x2). If Mo and MI are not homeomorphic, define dL(Mo,M1) = +00. Gromov [20] proves the remarkable result that the space of compact Riemannian manifolds L(A,t5 ,D) of sectional curvature IKI :::; A, injectivity radius i M 2: t5 >...

In this paper and in we study the structure of spaces Y which are pointed Gromov Hausdor limits of sequences f M i pi g of complete connected Riemannian manifolds whose Ricci curvatures have a de nite lower bound say RicMn i n In Sections and sometimes in we also assume a lower volume bound Vol B pi v In this case the sequence is said to be non collapsing If limi Vol B pi then the sequence is s...

A fundamental tool in the analysis of Ricci flow is a compactness result of Hamilton in the spirit of the work of Cheeger, Gromov and others. Roughly speaking it allows one to take a sequence of Ricci flows with uniformly bounded curvature and uniformly controlled injectivity radius, and extract a subsequence that converges to a complete limiting Ricci flow. A widely quoted extension of this re...

1 Introduction In a series of papers we develop a generalized Fredholm theory and demonstrate its applicability to a variety of problems including Floer theory, Gromov-Witten theory, contact homology, and symplectic field theory. Here are some of the basic common features: • The moduli spaces are solutions of elliptic PDE's showing serious non-compactness phenomena having well-known names like ...