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math.AP2013★ 13 cited
Fine properties of branch point singularities: Two-valued harmonic functions
Brian Krummel, Neshan Wickramasekera
In the 1980's, Almgren developed a theory of multi-valued Dirichlet energy minimizing functions on dimensional domains and used it, in an essential way, to bound the Hausdorff…
math.DG2013
Regularity of minimal hypersurfaces with a common free boundary
Brian Krummel
Let be a Riemannian manifold and consider a stationary union of three or more hypersurfaces-with-boundary in with a common boundary . We show that if …
math.DG2013
Existence and regularity of multivalued solutions to elliptic equations and systems
Brian Krummel
We extend the work of Simon and Wickramasekera, who constructed a large class of multivalued solutions to the minimal surface equation, to produce multivalued s…