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Geometric Analysis Seminar

The Bernstein problem for equations of minimal surface type

Connor Mooney (UC Irvine)

Location:  Zoom
Date & time: Tuesday, 19 October 2021 at 2:50PM - 3:50PM

Abstract: The Bernstein problem asks whether entire minimal graphs in
dimension N+1 are necessarily hyperplanes. This problem was solved in
combined works of Bernstein, Fleming, De Giorgi, Almgren, and Simons
("yes" if N < 8), and Bombieri-De Giorgi-Giusti ("no" otherwise). We
will discuss the analogue of this problem for graphical minimizers of
anisotropic energies. In particular, we will discuss new examples of
nonlinear entire graphical minimizers in the case N = 6, and recent
joint work with Y. Yang towards constructing such examples in the
lowest-possible-dimensional case N = 4.

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