English

$\sigma_k$-Yamabe measure

Analysis of PDEs 2024-07-26 v1

Abstract

We found a special divergence structure for the σk\sigma_k-Yamabe operator and use it to get a monotonicity formula. We also get an interior LL^{\infty} estimate via its L1L^1 norm for the σk\sigma_k-Yamabe operator when 1kn21\le k \le \frac{n}{2}. Combining these two tools, we prove the weak continuity of the σk\sigma_k-Yamabe measure with respect to convergence in measure.

Keywords

Cite

@article{arxiv.2407.17736,
  title  = {$\sigma_k$-Yamabe measure},
  author = {Xi-Nan Ma and Wangzhe Wu},
  journal= {arXiv preprint arXiv:2407.17736},
  year   = {2024}
}
R2 v1 2026-06-28T17:53:02.237Z