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020 _a9789349750555
040 _aNISER LIBRARY
_beng
_cNISER LIBRARY
082 _a514.7
_bALM-P
100 _aAlmgren, Frederick J.
245 _aPlateau's problem :
_ban invitation to varifold geometry
260 _aIndia :
_bUniversities Press,
_c2025.
300 _axiv, 78p. :
_bill. ;
_c22 cm.
490 _aStudent mathematical library,
_vv. 13
_x1520-9121 ;
504 _aIncludes bibliographical references and index.
520 _aThere have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book—or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films. When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encourage young mathematicians to study this fascinating subject further. Judging from the success of his students, it achieves this exceedingly well.
521 _aReadership: Advanced undergraduates and graduate students interested in mathematics.
650 _aMinimal surfaces
650 _aPlateau's problem
650 _aDifferential topology
856 _3Table of Contents
_uhttps://bookstore.ams.org/view?productcode=STML/13
856 _3Reviews
_uhttps://www.goodreads.com/book/show/2127174.Plateau_s_Problem?ref=nav_sb_ss_1_13#CommunityReviews
942 _2udc
_cN
999 _c36056
_d36056