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math.SP2024
Upper bound of the counting function of Steklov eigenvalues
Fei He, Lihan Wang
We study the counting function of Steklov eigenvalues on compact manifolds with boundary and obtain its upper bound involving the leading term of Weyl's law. Our estimate can be vi…
math.DG2024
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 b…
math.DG2024
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…