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Lecture Notes on Mean Curvature Flow
This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. These notes provide a detailed discussion of the classical parametric approach (mainly developed by R. Hamilton and G. Huisken). They are well suited for a course at PhD/PostDoc level and can be useful for any researcher interested in a solid introduction to the technical issues of the field. All the proofs are carefully written, often simplified, and contain several comments. Moreover, the author revisited and organized a large amount of material scattered around in literature in the last 25 years.
Mean Curvature Flow and Isoperimetric Inequalities
Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Diplomacy in Black and White
"This will be the first monograph-length study of U.S. diplomacy toward Saint-Domingue during the Adams administration. The book offers a detailed examination of the relationship between U.S. President John Adams and Toussaint Louverture, military commander of the French colony Saint-Domingue. Ronald Johnson presents the complex history of the bilateral relations between these two Atlantic leaders representing the first diplomatic relationship the United States had with a government of black leaders. Over the course of seven chapters, Johnson looks beyond the diplomacy itself to find the long lasting effects it had on the evolving meanings of race, the struggles over emancipation, and the fo...
Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations
The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.
Detective Fiction: the Novel
Is the drop-dead gorgeous psychiatrist in love or is some other far more nefarious plot afoot? The Journey pulls us in and leaves us wondering.Told she was schizophrenic at 19, it takes a trip to an unexpected homeland for the real truth to sink in: she is not crazy, but psychic.Raised by a degreed registered nurse and thus devoted to Western medicine, the hardest person to convince is herself, but by the end of Detective Fiction, the game between her self, her spiritual helpers, and the doppelganger who refuses to leave her alone becomes cold, calculating, and a clear risk to her survival.
Variational Problems in Riemannian Geometry
This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. There are introductory survey articles as well as papers presenting the latest research results. Among the topics covered are blow-up theory for second order elliptic equations; bubbling phenomena in the harmonic map heat flow; applications of scans and fractional power integrands; heat flow for the p-energy functional; Ricci flow and evolution by curvature of networks of curves in the plane.
Free Boundary Problems
Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.
A Perspective on Canonical Riemannian Metrics
This book focuses on a selection of special topics, with emphasis on past and present research of the authors on “canonical” Riemannian metrics on smooth manifolds. On the backdrop of the fundamental contributions given by many experts in the field, the volume offers a self-contained view of the wide class of “Curvature Conditions” and “Critical Metrics” of suitable Riemannian functionals. The authors describe the classical examples and the relevant generalizations. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.
Encyclopedia of Homosexuality
First published in 1990, The Encyclopedia of Homosexuality brings together a collection of outstanding articles that were, at the time of this book’s original publication, classic, pioneering, and recent. Together, the two volumes provide scholarship on male and female homosexuality and bisexuality, and, reaching beyond questions of physical sexuality, they examine the effects of homophilia and homophobia on literature, art, religion, science, law, philosophy, society, and history. Many of the writings were considered to be controversial, and often contradictory, at that time, and refer to issues and difficulties that still exist today. This volume contains entries from A-L.
