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Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle.
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
"Originally published in 1982, Stephen Shore's legendary Uncommon Places has influenced more than a generation of photographers. Shore was among the first artists to take color beyond the domain of advertising and fashion photography, and his large-format color work on the American vernacular landscape stands at the root of what has become a vital photographic tradition over the past forty years. Uncommon Places: The Complete Works, published by Aperture in 2004, presents a definitive collection of the landmark series, and in the span of a decade, has become a contemporary classic. Now, for this lushly produced reissue, the artist has added twenty rediscovered images and a statement explaining what it means to expand a series now many decades old. Like Robert Frank and Walker Evans before him, Shore discovered a hitherto unarticulated vision of America via highway and camera. Approaching his subjects with cool objectivity, Shore in these images retains precise internal systems of gestures in composition and light, through which a parking lot emptied of people, a hotel bedroom, or a building on a side street assumes both an archetypal aura and an ambiguously personal importance. In contrast to his signature landscapes with which Uncommon Places is often associated, this expanded survey reveals equally remarkable collections of interiors and portraits." -- Publisher's description.
Offers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.
The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. There is a rich and well-known theory of minimal surfaces. A surface whose mean curvature is constant but nonzero is obtained when we try to minimize the area of a closed surface without changing the volume it encloses. An easy example of a surface of constant mean curvature is the sphere. A nontrivial example is provided by the constant curvature torus, whose discovery in 1984 gave a powerful incentive for studying such surfaces. Later, many examples of constant mean curvature surfaces were discovered using various methods of analysis, differential geometry, and differential equations. It is now becoming clear that there is a rich theory of surfaces of constant mean curvature. In this book, the author presents numerous examples of constant mean curvature surfaces and techniques for studying them. Many finely rendered figures illustrate the results and allow the reader to visualize and better understand these beautiful objects. The book is suitable for advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.
In Surface Relations Vivian L. Huang traces how Asian and Asian American artists have strategically reworked the pernicious stereotype of inscrutability as a dynamic antiracist, feminist, and queer form of resistance. Following inscrutability in literature, visual culture, and performance art since 1965, Huang articulates how Asian American artists take up the aesthetics of Asian inscrutability—such as invisibility, silence, unreliability, flatness, and withholding—to express Asian American life. Through analyses of diverse works by performance artists (Tehching Hsieh, Baseera Khan, Emma Sulkowicz, Tseng Kwong Chi), writers (Kim Fu, Kai Cheng Thom, Monique Truong), and video, multimedia, and conceptual artists (Laurel Nakadate, Yoko Ono, Mika Tajima), Huang challenges neoliberal narratives of assimilation that erase Asianness. By using sound, touch, and affect, these artists and writers create new frameworks for affirming Asianness as a source of political and social critique and innovative forms of life and creativity. Duke University Press Scholars of Color First Book Award recipient
'Transparencies: Small Camera Works 1971-1979' offers an alternative account of one of the most fabled episodes in photographic history: the cross-country journeys that produced Stephen Shore's luminous new vision of the American landscape, 'Uncommon Places'. Along with his large-format camera, Shore also brought a 35mm Leica on his travels. The images made with it, on luminous colour slide film, are intimate, spontaneous and personal, while retaining Shore's studied formal sensitivity. In these entirely unseen photographs, a parallel iteration of an iconic vision emerges like a piece of music played in a new key. The vocabulary is familiar: highways and homes, phone boxes, fast food and sun-strewn parking lots. But the alternative format unmistakably re-envisions these subjects through distinct experiments with composition, attitude, and colour. Transparencies uncovers both a detail-oriented survey of the American landscape of the 1970s and a rigorous, imaginative exercise in form by an undisputed modern master. With an afterword by Britt Salvesen, curator at LACMA, titled 'Ordinary Speech: The Vernacular in Stephen Shore's Early 35mm Photography'.
Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.
Physics at Surfaces is a unique graduate-level introduction to the physics and chemical physics of solid surfaces, and atoms and molecules that interact with solid surfaces. A subject of keen scientific inquiry since the last century, surface physics emerged as an independent discipline only in the late 1960s as a result of the development of ultra-high vacuum technology and high speed digital computers. With these tools, reliable experimental measurements and theoretical calculations could at last be compared. Progress in the last decade has been truly striking. This volume provides a synthesis of the entire field of surface physics from the perspective of a modern condensed matter physicist with a healthy interest in chemical physics. The exposition intertwines experiment and theory whenever possible, although there is little detailed discussion of technique. This much-needed text will be invaluable to graduate students and researchers in condensed matter physics, physical chemistry and materials science working in, or taking graduate courses in, surface science.