For plurisubharmonic functions phi and psi lying in the Cegrell class of B-n and B-m respectively such that the Lelong number of phi at the origin vanishes, we show that the mass of the origin with respect to the measure (dd (c) max{phi(z), psi(Az)})(n) on C-n is zero for A is an element of Hom(C-n, C-m) = C-nm outside a pluripolar set. We establish a new approach and introduce a new concept coined the log truncated threshold of phi at 0 which reflects a singular property of phi via a log function near the origin (denoted by lt(phi, 0)), and derive an optimal estimate of the residual Monge-Amp & egrave;re mass of phi at 0 in terms of its higher order Lelong numbers nu(j)(phi) at 0 for 1 <= j <= n-1, in the case that lt(phi, 0) < infinity. These results unify and imply the well-known results about Guedj-Rashkovskii's zero mass conjecture.
Publication:
MATHEMATISCHE ANNALEN
http://dx.doi.org/10.1007/s00208-026-03474-w
Author:
Fusheng Deng
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
fshdeng@ucas.ac.cn
Yinji Li
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
liyinji@amss.ac.cn
Qunhuan Liu
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
liuqunhuan23@mails.ucas.edu.cn
Zhiwei Wang
Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
zhiwei@bnu.edu.cn
Xiangyu Zhou
Institute of Mathematics, State Key Laboratory of Mathematical Sciences, Chinese Academy of Sciences, 100190 Beijing, China
xyzhou@math.ac.cn
Publication:
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
http://dx.doi.org/10.1007/s10884-026-10494-2
Author:
Alexandru Hening
Department of Mathematics, Texas A&M University, College Station 77843-3368, US
Weiwei Qi
State Key Laboratory of Mathematical Sciences (SKLMS), Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
wwqi@amss.ac.cn
Zhongwei Shen
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB T6G 2G1, Canada
Yingfei Yi
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB T6G 2G1, Canada
yingfei@ualberta.ca
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