Luiz Henrique Lara dos Santos (LMBA)

On Some Rigidity Phenomena for Harmonic Maps

A common problem in mathematics, already familiar from calculus courses, is that of finding the points that minimize or maximize a given function. As one may recall, this problem is usually addressed in two steps, involving the study of the first and second derivatives of the function.

In this talk, we consider an analogue of this problem in a geometric setting, where the space of points is replaced by the space of smooth maps between two manifolds, and the function is the so-called Dirichlet energy functional.

We will discuss special maps characterized by the number of directions in which one can “move” from such a map in order to decrease the energy. This number is known as the Morse index.