This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Slawomir Kolodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Riviere, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.

This book gives a presentation of topics in Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject. The authors have aimed at presenting technical material in a clear and detailed manner. In this volume, geometric aspects of the theory have been emphasized. The book presents the theory of Ricci solitons, Kahler-Ricci flow, compactness theorems, Perelman's entropy monotonicity and no local collapsing, Perelman's reduced distance function and applications to ancient solutions, and a primer of 3-manifold topology. Various technical aspects of Ricci flow have been explained in a clear and detailed manner. The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to Perelman's work and explains technical aspects of Ricci flow useful for singularity analysis. Throughout, there are appropriate references so that the reader may further pursue the statements and proofs of the variou

This is the first comprehensive work in English on the complex history and theory of traditional Chinese narrative. It describes the major Chinese conventions and strategies for interpreting narrative works, both historical and fictional, from the earliest narratives through those of the Ch'ing dynasty. For most of China's recorded history, historical authenticity and factual accuracy were paramount in the production and reception of narrative texts. Fictional narratives were theorized and judged in accordance with the standards of historical narratives. In short, narrative was history, and fiction was defective history. Furthermore, the state made great efforts to control fiction by suppression (censorship) and disavowal (denigration and trivialization). It was only with the widespread popularity of novels in the Ming and Ch'ing dynasties that Chinese theorists were able to come to terms with fiction and dehistoricize the poetics of narrative by allowing and recognizing invention and fabrication in narrative texts. At this time, the Chinese poetics of narrative moved away from the long-held centrality of historicity, and critics acknowledged that good fiction can penetrate the nature and feelings of human beings in ways that other writings cannot, and that a reader is able to discover the uttermost principles of life in fiction just as in the Confucian classics and historical writings. Narrative was no longer assigned the function it had, for some 2,000 years, of being a "factual record" or "credible history." Its existence was justified because it conjured up a world that was lifelike and credible. In the process of tracing the long history of Chinese narrative, the author employs both Chinese and Western theoretical writings to chart convergences and differences in Chinese and Western literary theory and criticism.

This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Slawomir Kolodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Riviere, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.

This ambitious work is a multimedia, inter-disciplinary study of Chinese modernity in the context of globalization from the late nineteenth century to the present. Sheldon Lu draws on Chinese literature, film, art, photography, and video to broadly map the emergence of modern China in relation to the capitalist world-system in the economic, social, and political realms. Central to his study is the investigation of biopower and body politics, namely, the experience of globalization on a personal level. Lu first outlines the trajectory of the body in modern Chinese literature by focusing on the adventures, pleasures, and sufferings of the male (and female) body in the writings of selected authors. He then turns to avant-garde and performance art, tackling the physical self more directly through a consideration of work that takes the body as its very theme, material, and medium. In an exploration of mass visual culture, Lu analyzes artistic reactions to the multiple, uneven effects of globalization and modernization on both the physical landscape of China and the interior psyche of its citizens. This is followed by an inquiry into contemporary Chinese urban space in popular cinema and experimental photography and art. Examples are offered that capture the daily lives of contemporary Chinese as they struggle to make the transition from the vanishing space of the socialist lifestyle to the new capitalist economy of commodities. Lu reexamines the history and implications of China's belated integration into the capitalist world system before closing with a postscript that traces the genealogy of the term "postsocialism" and points to the real relevance of the idea for the investigation ofeveryday life in China in the twenty-first century.

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 Poincare conjecture and Thurston's geometrization conjecture.