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We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions.
Jonas Wiklund. "Matrix inequalities and the complex Monge-Ampère operator." Annales Polonici Mathematici 83.3 (2004): 211-220. <http://eudml.org/doc/280544>.
@article{JonasWiklund2004, abstract = {We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions.}, author = {Jonas Wiklund}, journal = {Annales Polonici Mathematici}, keywords = {complex Monge-Ampère equation; plurisubharmonic function; Lelong number}, language = {eng}, number = {3}, pages = {211-220}, title = {Matrix inequalities and the complex Monge-Ampère operator}, url = {http://eudml.org/doc/280544}, volume = {83}, year = {2004}, }
TY - JOUR AU - Jonas Wiklund TI - Matrix inequalities and the complex Monge-Ampère operator JO - Annales Polonici Mathematici PY - 2004 VL - 83 IS - 3 SP - 211 EP - 220 AB - We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions. LA - eng KW - complex Monge-Ampère equation; plurisubharmonic function; Lelong number UR - http://eudml.org/doc/280544 ER -