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2014•Proceedings of the American Mathematical SocietyOpen access

Manifolds with a weighted Poincaré inequality

Nguyen Thac Dung, Chiung-Jue Anna Sung

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Abstract

We study complete manifolds satisfying a weighted Poincaré type property. We establish a splitting and vanishing theorem for L 2 L^2 harmonic forms provided that the weight function ρ \rho is of exponential growth of the distance function. Our theory generalizes the results of Li-Wang, Lam and Chen-Sung.

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We study complete manifolds satisfying a weighted Poincaré type property. We establish a splitting and vanishing theorem for L 2 L^2 harmonic forms provided that the weight function ρ \rho is of exponential growth of the distance function. Our theory generalizes the results of Li-Wang, Lam and Chen-Sung.

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Available abstract

We study complete manifolds satisfying a weighted Poincaré type property. We establish a splitting and vanishing theorem for L 2 L^2 harmonic forms provided that the weight function ρ \rho is of exponential growth of the distance function. Our theory generalizes the results of Li-Wang, Lam and Chen-Sung.

Key concepts: Poincaré inequality, Mathematics, Pure mathematics, Property (philosophy), Harmonic function, Exponential function, Chen, Inequality

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