$\sigma_k$-Yamabe measure

Xi-Nan Ma; Wangzhe Wu

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arXiv · 2407.17736

$\sigma_k$-Yamabe measure

Xi-Nan Ma·Wangzhe Wu

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Abstract

We found a special divergence structure for the $\sigma_k$-Yamabe operator and use it to get a monotonicity formula. We also get an interior $L^{\infty}$ estimate via its $L^1$ norm for the $\sigma_k$-Yamabe operator when $1\le k \le \frac{n}{2}$. Combining these two tools, we prove the weak continuity of the $\sigma_k$-Yamabe measure with respect to convergence in measure.

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Xi-Nan Ma, Wangzhe Wu. 2024-07-25. $\sigma_k$-Yamabe measure. https://arxiv.org/abs/2407.17736

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