RIGIDITY PROPERTIES OF SMOOTH METRIC MEASURE SPACES VIA THE WEIGHTED p-LAPLACIAN.

In this paper, we show sharp estimates for the first eigenvalue λ1,p of the weighted p-Laplacian on smooth metric measure spaces (M, g, e−f dv). When the Bakry-Émery curvature Ricf is bounded from below and the weighted function f is of sublinear growth, we prove some rigidity properties provided that the first eigenvalue λ1,p obtains its optimal value. [ABSTRACT FROM AUTHOR]