Geometric Analysis and Topology Seminar

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On polynomial solutions to the minimal surface equation

Speaker: Yifan Guo, NYU

Location: Warren Weaver Hall 512

Date: Friday, September 5, 2025, 11 a.m.

Synopsis:

We study nonlinear polynomial solutions to the minimal surface equation on R^n. Although no explicit solutions are obtained, we analyze the structural constraints such polynomials must satisfy by making use of the area-minimizing property. In particular, we establish a structure theorem describing the factorization of the leading-order term. Using the structure theorem, we derive restrictions on the possible degree of the polynomial, and the tangent cone associated with a polynomial solution. These results reveal that the form of any polynomial solution is highly restricted.