The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on November 21, 2017  at 2 p.m. in Room 478 of IMI.

A talk on:

On the geometry of minimal surfaces in four-dimensional Euclidean or Minkowski space

will be delivered by Krasimir Kanchev, Higher Transport School “Todor Kableshkov”, Sofia.

Everybody is invited.

Abstract. We prove that any minimal surface in n-dimensional Euclidean or Lorentz space locally admits geometrically determined parameters - canonical parameters. For any minimal surface of general type in four-dimensional Euclidean or Minkowski space parametrized by canonical parameters we obtain Weierstrass representations - canonical Weierstrass representations. These formulas allow us to solve explicitly the system of natural partial differential equations and to establish geometric correspondence between minimal surfaces of general type, the solutions to the system of natural partial differential equations and pairs of holomorphic functions in the Gauss plane. On the base of these correspondences we obtain that any minimal surface of general type in Euclidean 4-space determines locally a pair of two minimal surfaces in Euclidean 3-space and vice versa.