Suppose that there exist two Kähler metrics ω and α such that the metric contraction of α with respect to ω is constant, i.e. Λωα = const. We prove that for all large enough R > 0 there exists a twisted constant scalar curvature Kähler metric ω ′ in the cohomology class [ω], satisfying S(ω ′ ) − RΛ ω ′ α = const. We discuss its implication to K-stability and the continuity method recently proposed by X.X. Chen.
Although (+)-catharanthine
is an attractive alkaloid for both clinical
research and organic synthetic chemistry, only a limited number of
approaches for its catalytic asymmetric synthesis exist. Herein, we
describe a novel strategy for synthesizing a chiral intermediate of
(+)-catharanthine via phosphoric acid-catalyzed asymmetric desymmetrization
of a meso-isoquinuclidine possessing a 1,3-diol unit
that was synthesized by a formal amide insertion reaction.
Suppose that a polarised Kähler manifold (X, L) admits an extremal metric ω. We prove that there exists a sequence of Kähler metrics {ω k } k , converging to ω as k → ∞, each of which satisfies the equation ∂grad 1,0 ω k ρ k (ω k ) = 0; the (1, 0)-part of the gradient of the Bergman function is a holomorphic vector field.
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