Convexity of the first eigenfunction of the drifting Laplacian operator and its applications
نویسندگان
چکیده
In this short note, we prove 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. After giving a gradient estimate, we then use the convexity of the first eigenfunction to get a lower bound of the difference of the first and second eigenvalues of the drifting Laplacian.
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