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Smooth metric measure spaces with weighted Poincaré inequality

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Abstract

In this paper, we study smooth metric measure space (M, g, e −f dv) satisfying a weighted Poincaré inequality and establish a rigidity theorem for such a space under a suitable Bakry–Émery curvature lower bound. We also consider the space of f-harmonic functions with finite energy and prove a structure theorem.

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Authors and Affiliations

  1. Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan, ROC

    Nguyen Thac Dung & Chiung Jue Anna Sung

Authors
  1. Nguyen Thac Dung
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  2. Chiung Jue Anna Sung
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Correspondence to Chiung Jue Anna Sung.

Additional information

N. T. Dung was partially supported by the grant NAFOSTED 101.01-2011.13.

C. J. A. Sung was partially supported by NSC.

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Dung, N.T., Sung, C.J.A. Smooth metric measure spaces with weighted Poincaré inequality. Math. Z. 273, 613–632 (2013). https://doi.org/10.1007/s00209-012-1023-y

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  • DOI: https://doi.org/10.1007/s00209-012-1023-y

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