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The Ricci Flow: An Introduction
The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to 'flow' a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics. Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program. The Ricci flow method is now central to our understanding of the geometry and topology of ma...
Hamilton’s Ricci Flow
Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.
Truth and Dare
A memoir of a promising leading actress who inexplicitly vanished from the public view: the journey of female ambition with reflections on women's disempowerment at work, home, and society weaved through socio-economical changes. Relatable and exceptional accounts of a small family business, worldly adventures, class, and marital struggles.
Inequalities in Geometry and Applications
This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.
Rotifera IX
This volume is a record of the proceedings of the IXth International Rotifer Symposium, which was held in Khon Kaen, Thailand, on January 16-23, 2000. The symposium was the first meeting of the international group of rotifer researchers held in Asia. The volume contains reviews and research papers dealing with diverse aspects of scientific research related to Rotifera and their ecology. Some of the topics addressed are: taxonomy and zoogeography, ecology, phylogeny and evolution, physiology, biochemistry and population genetics, aquaculture, and ecotoxicology. This book is special because it contains a unique compilation of contemporary rotifer-related research, and is the eighth of a series of rotifer symposium proceedings published in Developments of Hydrobiology. This update of Rotifera studies will be of great interest to invertebrate zoologists, hydrobiologists, ecologists, and aquaculturists, particularly those interested in freshwater habitats.
Past Societies
From the North Atlantic to the Persian Gulf and from Peru to the Near East, this book illustrates different studies on the interfluve of environments and societies in landscapes and describes certain historical moments and processes in which the interplay of ecological and societal factors is entangled.
Glimpses of Soliton Theory
Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --
Generalized Ricci Flow
The generalized Ricci flow is a geometric evolution equation which has recently emerged from investigations into mathematical physics, Hitchin's generalized geometry program, and complex geometry. This book gives an introduction to this new area, discusses recent developments, and formulates open questions and conjectures for future study.The text begins with an introduction to fundamental aspects of generalized Riemannian, complex, and Kähler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures as.
