arXiv subjects

Kwan-hang Lam

Publications and source records attributed to Kwan-hang Lam.

2 recordsLinked to original sources

arXiv2007

Spectrum of the Laplacian on manifolds with Spin(9) holonomy

We consider noncompact complete manifolds with Spin(9) holonomy and proved an one end result and a splitting type theorem under different conditions on the bottom of the spectrum. We proved that any harmonic functions with finite Dirichlet integral must be Cayley-harmonic, which allowed us to conclude an one end result. In the second part, we established a splitting type theorem by utilizing the Busemann function..

math.DG↗

arXiv2007

Finiteness and vanishing results on weighted Poincare inequality of complete manifolds

We study manifolds satisfying a weighed Poincare inequality, which was first introduced by Li-Wang. We generalized one of their results by relaxing the Ricci curvature bound condition only being satisfied outside a compact set and established a finitely many ends result. We proved a vanishing result for $L^2$ harmonic 1-form provided that the weight function $ρ$ is of sub-quadratic growth of the distance function.

math.DG↗