Convex eigenfunction of a drifting Laplacian operator and the fundamental gap

• Autores: Li Ma, Baiyu Liu
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 240, Nº 2, 2009, págs. 343-361
• Idioma: inglés
• DOI: 10.2140/pjm.2009.240.343
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• Resumen

  • 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.