Metrics On $S^2$ With Bounded $\|K_g\|_{L^1\log L^1}$ And Small $\|K_g-1\|_{L^1}$

Yuxiang Li; Hongyan Tang

paper

Metrics On $S^{2}$ With Bounded $∥ K_{g} ∥_{L^{1} l o g L^{1}}$ And Small $∥ K_{g} - 1 ∥_{L^{1}}$

arXiv:1712.08943

Abstract

In this short paper, we will study the convergence of a metric sequence $g_{k}$ on $S^{2}$ with bounded $\int ∣ K_{g_{k}} ∣ lo g (1 + ∣ K_{g_{k}} ∣) d μ_{g_{k}}$ and small $\int ∣ K (g_{k}) - 1∥ d μ_{g_{k}}$ . We will show that such a sequence is precompact.

References in corpus (1)

Conformal metric sequences with integral-bounded scalar curvature

Metrics On S2 With Bounded ∥Kg​∥L1logL1​ And Small ∥Kg​−1∥L1​

Abstract

References in corpus (1)

Metrics On $S^{2}$ With Bounded $∥ K_{g} ∥_{L^{1} l o g L^{1}}$ And Small $∥ K_{g} - 1 ∥_{L^{1}}$