4 papers · 1 filter
Spectral bounds for -Laplace-type operators with applications to Betti numbers on gradient Ricci shrinkers
Fei He
We study the spectrum of the -Laplacian on complete gradient Ricci shrinkers. Upper and lower bounds for the -th eigenvalue are established in terms of the volume growth rate…
The dimension of polynomial growth holomorphic functions and forms on gradient Kähler Ricci shrinkers
Fei He, Jianyu Ou
We study polynomial growth holomorphic functions and forms on complete gradient shrinking Ricci solitons. By relating to the spectral data of the -Laplacian, we show that the di…
Topology of gradient Ricci shrinkers via weighted cohomology
Fei He
This paper proves several topological results for smooth gradient Ricci shrinkers. We establish upper bounds for the Betti numbers, a vanishing theorem for cohomology, and a dichot…
Dimension estimate and existence of holomorphic sections with polynomial growth on gradient Kähler Ricci shrinkers
Fei He, Jianyu Ou
We prove an upper bound for the dimension of the linear space of holomorphic functions with polynomial growth on gradient Kähler Ricci shrinkers with bounded curvature. The upper…