Geometry and Topology Seminar

In this talk we'll discuss a 1-to-1 correspondence between Euclidean minimal and Bryant surfaces, known in the literature as Lawson's correspondence. Along this correspondence we will study framed surfaces, which is a class of Euclidean minimal and hyperbolic CMC-1 surfaces that generalize immersed Euclidean minimal surfaces and Bryant surfaces. For this class we prove a lower bound on the (unrestricted) Morse index by a linear function of the genus, number of ends and number of branch points (counting multiplicity), generalizing previous work in the literature. This is based on joint work with Davi Maximo.