University of Pittsburg|
In the first part of the talk, we go over a brief introduction of harmonic maps. Sacks-Uhlenbeck and Shoen’s results are well-known applications of harmonic map theory. In 1984 Schoen conjectured that there is a unique minimal surface in a product of n Riemann surfaces with homotopy restriction, where n is bigger than 2. In 2022, Markovic showed this is false. In the later part of the talk I will briefly describe how Markovic disproved the Schoen conjecture.