The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds

2018/05/24 by Chen, Xuezhang, Ruan, Yuping, Sun, Liming · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.09597

Abstract

The Han-Li conjecture states that: Let (M,g₀) be an n-dimensional (n≥ 3) smooth compact Riemannian manifold with boundary having positive (generalized) Yamabe constant and c be any real number, then there exists a conformal metric of g₀ with scalar curvature 1 and boundary mean curvature c. Combining with Z. C. Han and Y. Y. Li's results, we answer this conjecture affirmatively except for the case that n≥ 8, the boundary is umbilic, the Weyl tensor of M vanishes on the boundary and has a non-zero interior point.

Cited by

• Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu)
• Blow-up phenomena for a boundary Yamabe problem with umbilic boundary

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