On the geometric flows solving Kählerian inverse $σ_k$ equations

Details On the geometric flows solving Kählerian inverse $σ_k$ equations On the geometric flows solving Kählerian inverse $σ_k$ equations

2012-03-12

arxiv.org/abs/1203.2571v1

Mathematics

Differential Geometry

to appear in Pacific Journal of Mathematics

Scientific paper

In this note, we extend our previous work on the inverse $\sigma_k$ problem.
Inverse $\sigma_{k}$ problem is a fully nonlinear geometric PDE on compact
K\"ahler manifolds. Given a proper geometric condition, we prove that a large
family of nonlinear geometric flows converges to the desired solution of the
given PDE.

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