Geometric Measure Theory and Minimal Surfaces : Lectures Given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Varenna (Como), Italy, August 24 - September 2, 1972

W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi’s measure and thin obstacles. Cover......Page 1 Geometric\rMeasure Theory and\rMinimal Surfaces......Page 2 ISBN 9783642109690......Page 3 Contents......Page 4 On The First Variation of Area and Generalized Mean Curvature......Page 5 Lecture One......Page 6 Lecture Two......Page 15 Lecture Three......Page 19 Lecture Four......Page 28 References......Page 33 Geometric Measure Theory and Elliptic Variational, Problems......Page 35 Some phenomena of geometric variational problems......Page 38 Goomotric variational problems in a mapping setting and associated varifolds......Page 52 Surfaces as measures......Page 64 A regularity theorem......Page 72 Estimates on singular sets......Page 75 Caratheodory's construction for k dimensional measures in R n and the atructure of sets of finite of finite Hausdorff measure......Page 78 References......Page 98 Introduction......Page 121 1. Smooth obstacles......Page 123 2. Discontinuous and thin obstacles; existences theory......Page 134 3. Regularity of the attainable solution; the favorable case......Page 141 4. Regularity of the attainable solution; the general case......Page 144 References......Page 150 Singularities in Soap-Bubble-Link and Soap-Film-Link Surfaces......Page 155 References......Page 165 Figure 1......Page 166 Figure 3......Page 167 Figure 4......Page 168 Figure 5......Page 169 The Analyticity of the Coincidence Set in Variational Inequalities......Page 170 References......Page 183 Boundaries of Caccioppoli Sets in the Calculus of Variations......Page 185 Bibliography......Page 212 De Giorgi's Measure and Thin Obstacles......Page 216 References......Page 223 Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.Æs activities over the years. The main purpose and mode of functioning of the Centre may be summarised as follows: every year, during the summer, sessions on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. A Session is generally based on three or four main courses given by specialists of international renown, plus a certain number of seminars, and is held in an attractive rural location in Italy The aim of a C.I.M.E. session is to bring to the attention of younger researchers the origins, development, and perspectives of some very active branch of mathematical research. The topics of the courses are generally of international resonance. The full immersion atmosphere of the courses and the daily exchange among participants are thus an initiation to international collaboration in mathematical research. --Book Jacket C.I.M.E. stands for Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Centre. Conceived in the early fifties, it was born in 1954 in Florence, Italy, and welcomed by the world mathematical community: it continues successfully, year for year, to this day