Vanishing theorems of 𝐿²-cohomology groups on Hessian manifolds

抄録

We show vanishing theorems of 𝐿²-cohomology groups of Kodaira–Nakano type on complete Hessian manifolds by introducing a new operator ∂'_𝐹. We obtain further vanishing theorems of 𝐿²-cohomology groups $𝐿^2 𝐻^{𝑝,𝑞}_{\bar{∂}}(Ω)$ on a regular convex cone Ω with the Cheng–Yau metric for 𝑝 > 𝑞.