$σ_k$-Yamabe measure
Xi-Nan Ma, Wangzhe Wu · arXiv (Cornell University) · 2024
We found a special divergence structure for the $σ_k$-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 $σ_k$-Yamabe operator when $1\le k \le \frac{n}{2}$. Combining these two tools, we prove the weak continuity of the $σ_k$-Yamabe measure with respect to convergence in measure.