On existence of the prescribing k-curvature of the Einstein tensor

2018/11/05 by Bo, Leyang, Sheng, Weimin
#35J60 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.01646

Abstract

In this paper, we study the problem of conformally deforming a metric on a 3-dimensional manifold M³ such that its k-curvature equals to a prescribed function, where the k-curvature is defined by the k-th elementary symmetric function of the eigenvalues of the Einstein tensor, 1≤ k≤ 3. We prove the solvability of the problem and the compactness of the solution sets on manifolds when k=2 and 3, provided the conformal class admits a negative k-admissible metric with respect to the Einstein tensor.

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