By W. K. Allard (auth.), Prof. E. Bombieri (eds.)
W.K. ALLARD: at the first edition of quarter and generalized suggest curvature.- F.J. ALMGREN Jr.: Geometric degree concept and elliptic variational problems.- E. GIUSTI: minimum surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the twist of fate set in variational inequalities.- M. MIRANDA: limitations of Caciopoli units within the calculus of variations.- L. PICCININI: De Giorgi’s degree and skinny obstacles.
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Extra info for Geometric Measure Theory and Minimal Surfaces
Ir most natural setting[BJ]. (b) Various long standing qu es t i on s in the theory of Lebesgue area have 'be en settled [FH3].
Roughly speaking the "direct method" makes sense in a variational problem when the formulation of the problem itself guarantees the existence of a sequence (fiji of mappings in ~, any sui tabl e convergent (in ~) subsequence of whi ch would yi el d a s olutlon to the problem; - 56 - F. J. Almgren Jr. ) 1 1 inf ! ~ fact admit subsequences convergent to solutions. The main difficulties wh i ch I know about in the attempt "0 use the direct method in geometric variational problems seem best illustrated by examples.
J. Almgren Jr. There are six partsl PART A. Some phenomena of geometric variational problems. PART B. Geometric variational problems in a mapping setting and associated varifolds. PART C. Surfaces as measures. PART D. A regularity theorem. PART E. Estimates on singular sets. PART F. Caratheodory1s con struction for k dime nsional measure s in Rn and the structure of sets of finite Hau s dorff me a su r e . There a r e also twenty illustrations. Figure 1. A disk with five han dl e s . Figure 2. A s impl e closed unknotted boun dary cu rve C of f inite length.