Theorems on the Regularity and Singularity of Minimal Surfaces and Harmonic Maps
These lectures are meant as an introduction to the analytic aspects of the study of regularity properties and singularities of minimal surfaces and harmonic maps.
KeywordsMinimal Surface Approximation Property Compactness Theorem Regularity Theorem Lipschitz Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- [A1]F. Almgren, Q-valued functions minimizing Dirichlet’s integral and the regularity of of area minimizing rectifiable currents up to codimension two, Preprint.Google Scholar
- [B]F. Bethuel, On the singular set of stationary harmonic maps, PreprintGoogle Scholar
- [DeG]E. De Giorgi, Frontiere orientate di misura minima, Sem. Mat. Scuola Norm. Sup. Pisa (1961), 1-56.Google Scholar
- [GT]D. Gilbarg & N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983.Google Scholar
- [HL1]R. Hardt & F.-H. Lin, The singular set of an energy minimizing harmonic map from B 4 to S 2, Preprint 1990.Google Scholar
- [JJ]J. Jost, Harmonic maps between Riemannian manifolds, Proceedings of the Centre for Mathematical Analysis, Australian National University, 3 (1984).Google Scholar
- [L]S. Lojasiewicz, Ensembles semi-analytiques, IHES notes (1965).Google Scholar
- [Lu2]S. Luckhaus, Convergence of Minimizers for the p-Dirichlet Integral, Preprint, 1991.Google Scholar
- [MCB]C. B. Morrey, Multiple integrals in the calculus of variations, Springer Verlag, 1966.Google Scholar
- [Riv]E. Riviere, Everywhere discontinuous maps into the sphere, Preprint.Google Scholar
- [SL1]L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, 3 (1983).Google Scholar
- [SL3]L. Simon, On the singularities of harmonic maps, In preparation.Google Scholar
- [SL4]L. Simon, Singularities of Geometric Varational Problems, Summer School Lectures delivered at RGI, Park City, Utah, 1992, To appear in AMS Park City Geometry Series.Google Scholar
- [SL5]L. Simon, Proof of the Basic Regularity Theorem for Harmonic Maps, Summer School Lectures delivered at RGI, Park City, Utah, 1992, To appear in AMS Park City Geometry Series.Google Scholar
- [SL7]L. Simon, Lectures on regularity and singularity of energy minimizing maps: Monograph to appear in ETH Lectures in Mathematics series, BirkhäuserGoogle Scholar
- [SL8]L. Simon, Rectifiability of the singular set of energy minimizing maps, To appear in Calculus of Variations and PDE.Google Scholar
- [SL9]L. Simon, Rectifiability of the singular set of multiplicity 1 minimal surfaces, To appear in Surveys of Differential Geometry.Google Scholar
© Springer-Verlag Tokyo 1996