Convex eigenfunction of a drifting Laplacian operator and the fundamental gap
Convex eigenfunction of a drifting Laplacian operator and the fundamental gap
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 …