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Complex Hessian Operator and Generalized Lelong Numbers Associated to a Closed m-Positive Current

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Abstract

In this paper, we first introduce the generalized Lelong number of an m-positive current T with respect to an m-subharmonic weight \(\varphi \). We also prove two Demailly’s comparison theorems of the generalized Lelong numbers. Then by establishing an estimate for m-capacity \(cap_{m,T}\), we show a new expression of the generalized Lelong number in terms of the \(cap_{m,T}\)-capacity of the sublevel set of \(\varphi \).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Shenzhen University, Room 415, Science and Technology Building, Shenzhen, 518060, People’s Republic of China

    Dongrui Wan

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  1. Dongrui Wan
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Correspondence to Dongrui Wan.

Additional information

Communicated by Ahmed Sebbar.

This work is supported by National Nature Science Foundation in China (Nos. 11401390, 11571305).

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Wan, D. Complex Hessian Operator and Generalized Lelong Numbers Associated to a Closed m-Positive Current. Complex Anal. Oper. Theory 12, 475–489 (2018). https://doi.org/10.1007/s11785-017-0711-3

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