Affiliation:
1. Department of Mathematics , Institut de Mathématiques de Jussieu-Paris Rive Gauche , Paris , France
Abstract
Abstract
Let X be a compact Kähler manifold.
Fix a big
(
1
,
1
)
{(1,1)}
-cohomology class α with smooth representative θ.
We study the spaces
ℰ
p
(
X
,
θ
)
{\mathcal{E}^{p}(X,\theta)}
of finite energy Kähler potentials for each
p
≥
1
{p\geq 1}
.
We define a metric
d
p
{d_{p}}
without using the Finsler geometry nor solving Monge–Ampère-type equations. This construction generalizes the usual
d
p
{d_{p}}
-metric defined for an ample class.
Funder
Knut och Alice Wallenbergs Stiftelse
Subject
Applied Mathematics,General Mathematics
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