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A course in minimal surfaces / |
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ISBN/ISSN:
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9780821853238 (alk. paper) |
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ISBN/ISSN:
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0821853236 (alk. paper) |
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中图分类法
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O186.16 |
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著者:
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Colding, Tobias H. |
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题名:
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A course in minimal surfaces / |
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出版发行:
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Providence, R.I. : American Mathematical Society, c2011. |
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载体形态:
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xii, 313 p. : ill. (some col.) ; 27 cm. |
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内容提要:
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"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."--Publisher's description. |
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主题词:
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Minimal surfaces. |
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主要责任者:
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Minicozzi, William P. |
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HEA| |01925cam a2200277 a 4500 001| |022011000607 003| |OCoLC 005| |20110616123345.0 008| |101101s2011 riua b 001 0 eng 020| |▼a9780821853238 (alk. paper) 020| |▼a0821853236 (alk. paper) 035| |▼a(OCoLC)677972650 040| |▼aDLC▼cDLC▼dYDX▼dYDXCP▼dCTB▼dU- | |BY▼dCDX▼dBGU 042| |▼apcc 050|00|▼aQA644▼b.C648 2011 082|00|▼a516.3/62▼222 093| |▼aO186.16▼25 100|1 |▼aColding, Tobias H. 245|12|▼aA course in minimal surfaces- | | /▼cTobias Holck Colding, Will- | |iam P. Minicozzi II. 260| |▼aProvidence, R.I. :▼bAmerican- | | Mathematical Society,▼cc2011. 300| |▼axii, 313 p. :▼bill. (some co- | |l.) ;▼c27 cm. 490|0 |▼aGraduate studies in mathemat- | |ics ;▼vv. 121. 504| |▼aIncludes bibliographical ref- | |erences and index. 520| |▼a"Minimal surfaces date back - | |to Euler and Lagrange and the - | |beginning of the calculus of v- | |ariations. Many of the techniq- | |ues developed have played key - | |roles in geometry and partial - | |differential equations. Exampl- | |es include monotonicity and ta- | |ngent cone analysis originatin- | |g in the regularity theory for- | | minimal surfaces, estimates f- | |or nonlinear equations based o- | |n the maximum principle arisin- | |g in Bernstein\'s classical wor- | |k, and even Lebesgue\'s definit- | |ion of the integral that he de- | |veloped in his thesis on the P- | |lateau problem for minimal sur- | |faces. This book starts with t- | |he classical theory of minimal- | | surfaces and ends up with cur- | |rent research topics. Of the v- | |arious ways of approaching min- | |imal surfaces (from complex an- | |alysis, PDE, or geometric meas- | |ure theory), the authors have - | |chosen to focus on the PDE asp- | |ects of the theory. The book a- | |lso contains some of the appli- | |cations of minimal surfaces to- | | other fields including low di- | |mensional topology, general re- | |lativity, and materials scienc- | |e."－－Publisher\'s description. 650| 0|▼aMinimal surfaces. 700|1 |▼aMinicozzi, William P.
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