A definitive majorization result for nonlinear operators

2024/07/07 by Harvey, F. Reese, Lawson, H. Blaine · 1 citation
#32Q25 #32W20 #35A23 #35B45 #35B65 #35G20 #53C55 #58J32 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.05408

Abstract

Let \mathfrak g be a Garding-Dirichlet operator on the set S(n) of symmetric n× n matrices. We assume that \mathfrak g is I-central, that is, D_I \mathfrak g = k I for some k>0. Then \mathfrak g(A)^{1\over N} ≥ \mathfrak g(I)^{1\over N} (det A)^{1\over n} ∀ Agt;0. From work of Guo, Phong, Tong, Abja, Dinew, Olive and many others, this inequality has important applications.

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