Speaker：Prof. Guowei Dai，Dalian University of Technology

Title: Global bifurcation of the mean curvature equation in certain Friedmann-Lemaître-Robertson-Walker spacetimes

Abstract: In this talk, we will talk about the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz-Minkowski spacetime. Then, by using Rabinowitz`s global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied. This is based on joint work with Professors Alfonso Romero and Pedro J. Torres.