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arXiv · 1811.01646

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

Leyang Bo·Weimin Sheng
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Abstract

In this paper, we study the problem of conformally deforming a metric on a $3$-dimensional manifold $M^3$ 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, $1\le k\le 3$. 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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Leyang Bo, Weimin Sheng. 2018-11-05. On existence of the prescribing $k$-curvature of the Einstein tensor. https://arxiv.org/abs/1811.01646

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