Jenkins-Serrin problem for translating graphs A translating soliton is a smooth oriented hypersurface S in MxR (or in Rn+1) whose mean curvature satisfies H = <X,N>, where X is a given vector and N denotes the unit normal to the surface S. In the case S is a graph of a function u, u satisfies the so-called translating soliton equation and S will be called a translating graph. These solitons play an important role in the study of the singularities of the mean curvature flow, but recently they have gained also a lot of interest on their own. On the other hand, the Jenkins-Serrin problem asks for solutions (of certain PDE) to a Dirichlet problem on a domain D such that the boundary data can be also infinite on some parts of the boundary of D. This problem has been considered earlier e.g. for the minimal surfaces but in this talk I will discuss about existence results for the translating soliton equation in Riemannian products MxR. The talk is based on recent joint works with E.S. Gama, J. de Lira and F. Martín. |