Resumen de Convex eigenfunction of a drifting Laplacian operator and the fundamental gap

Li Ma, Baiyu Liu

• We study the convexity of the first eigenfunction of the drifting Laplacian operator with zero Dirichlet boundary value provided a suitable assumption to the drifting term is added. We firstly generalize some results of N. Korevaar and S.-T. Yau to gain a Hessian estimate of the first eigenfunction. As an application, we use this Hessian estimate to get a lower bound of the difference of the first and second eigenvalues of the drifting Laplacian. At the end we also find a lower bound when the Hessian estimate does not hold.