Yenni Cherik

Let (X,0) be a complex surface germ with an isolated singularity at the origin of C^n and f:(X,0)->(C,0) be a non constant holomorphic function. We will study the inner metric of the Milnor fibers f^(-1)(t) by defining a family of metric invariants called inner-rates. After  that i will state and prove the inner-rates formula which provide us a concrete way of computing the inner rates and, on the other hand, relate them with the polar curves of f. We will end the talk with an application of the inner rates to compute the integral of the gaussian curvature on the Milnor fibers.