Determinant majorization and the work of Guo-Phong-Tong and Abja-Olive

作者：F. R. Harvey, H. Lawson · 年份：2022 · 被引用次数：19 · 研究领域：Mathematics

. The objective of this note is to establish the Determinant Majorization Formula F ( A ) 1 N ≥ det( A ) 1 n for all operators F determined by an invariant G˚arding-Dirichlet polynomial of degree N on symmetric n × n matrices. Here invariant means under the group O( n ), U( n ) or Sp( n ) when the matrices are real symmetric, Hermitian symmetric, or quaternionic symmetric respectively. This greatly expands the applicability of the recent work of Guo-Phong-Tong and Guo-Phong for differential equations on complex manifolds. It also relates to the work of Abja-Olive on interior regularity.