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math.DG2024
Continuity method for the Mabuchi soliton on the extremal Fano manifolds
Tomoyuki Hisamoto, Satoshi Nakamura
We run the continuity method for Mabuchi's generalization of Kähler-Einstein metrics, assuming the existence of an extremal Kähler metric. It gives an analytic proof (without minim…
math.DG2024★ 1 cited
On the Miyaoka-Yau inequality for manifolds with nef anti-canonical line bundle
Tomoyuki Hisamoto
Based on the recent work of K.~Zhang, we discuss the Miyaoka-Yau type inequality for projective manifolds with nef anti-canonical line bundle, assuming the lower bound of the delta…
math.DG2024
Quantization of the Kähler-Ricci flow and optimal destabilizer for a Fano manifold
Tomoyuki Hisamoto
For a Fano manifold, We consider the geometric quantization of the Kähler-Ricci flow and the associated entropy functional. Convergence to the original flow and entropy is establis…