Measures on spaces of surfaces

DOI10.1007/BF00249585zbMath0529.58031MaRDI QIDQ787563

Frank Morgan

Publication date: 1982

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

geometric measure theorycircular Brownian motionprobability measure on function space

Mathematics Subject Classification ID

Brownian motion (60J65) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Pseudodifferential and Fourier integral operators on manifolds (58J40) Length, area, volume, other geometric measure theory (28A75) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12) Probability theory on algebraic and topological structures (60B99) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

Related Items

Size-minimizing rectifiable currents ⋮ The isoperimetric problem in higher codimension ⋮ Gaussian measures on the of space of Riemannian metrics ⋮ Generic uniqueness for the Plateau problem ⋮ Averaged pointwise bounds for deformations of Schrödinger eigenfunctions ⋮ Scalar curvature and \(Q\)-curvature of random metrics ⋮ Calibrations and the size of Grassmann faces ⋮ Harmonic maps with fixed singular sets

Cites Work

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• Gaussian measures in Banach spaces
• On the first variation of a varifold: Boundary behavior
• A smooth curve in \(R^4\) bounding a continuum of area minimizing surfaces
• Almost every curve in \(R^3\) bounds a unique area minimizing surface
• Diffusion processes and their sample paths.
• The spectral function of an elliptic operator
• On sets of Haar measure zero in abelian Polish groups
• On equivalence of infinite product measures
• Minimal varieties
• The Resolvent of an Elliptic Boundary Problem
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
• Random Fourier Transforms

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