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Zhou, Xiangyu; Zhu, Langfeng

Optimal \(L^2\) extension of sections from subvarieties in weakly pseudoconvex manifolds. (English) Zbl 1458.32013

Pac. J. Math. 309, No. 2, 475-510 (2020).
Summary: We obtain optimal \(L^2\) extension of holomorphic sections of a holomorphic vector bundle from subvarieties in weakly pseudoconvex Kähler manifolds. Moreover, in the case of a line bundle the Hermitian metric is allowed to be singular.

Cited in 13 Documents

MSC:

32D15 Continuation of analytic objects in several complex variables
32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
32Q15 Kähler manifolds
32U05 Plurisubharmonic functions and generalizations
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators

Keywords:

optimal \(L^2\) extension; plurisubharmonic function; multiplier ideal sheaf; strong openness; weakly pseudoconvex manifold; Kähler manifold
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References:

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