Minimal surfaces with micro-oscillations
classification
🧮 math.DG
math.AP
keywords
minimalgeometrygraphssmallwhosealmostballconstruction
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We show that there are minimal graphs in R^{n+1} whose intersection with the portion of the horizontal hyperplane contained in the unit ball has any prescribed geometry, up to a small deformation. The proof hinges on the construction of minimal graphs that are almost flat but have small oscillations whose geometry we can control.
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