paneitz operator造句

例句与造句

1. The Paneitz operator appears in extremal problems for the Moser & ndash; Trudinger inequality in dimension four as well
2. One can ask if all compactly embedded CR manifolds in \ mathbb { C } ^ 2 have non-negative Paneitz operators.
3. The Paneitz operator has been most thoroughly studied in dimension four where it appears naturally in connection with extremal problems for the functional determinant of the Laplacian ( via the Polyakov formula; see ).
4. In dimension four only, the Paneitz operator is the " critical " GJMS operator, meaning that there is a residual scalar piece ( the Q curvature ) that can only be recovered by asymptotic analysis.
5. One of the principal applications of the CR Paneitz operator and the results in [ 3 ] are to the CR analog of the Positive Mass theorem due to Jih-Hsin Cheng, Andrea Malchiodi and Paul C . Yang.
6. It's difficult to find paneitz operator in a sentence. 用paneitz operator造句挺难的
7. That is, if one starts with a family of compact CR manifolds embedded in \ mathbb { C } ^ 2, and the CR structure of the family J _ t changes in a real-analytic way with respect to the parameter t, and the CR Yamabe constant of the family of manifolds is uniformly bounded below by a positive constant, then the CR Paneitz operator remains non-negative for the entire family, provided one member of the family has its CR Paneitz operator non-negative.
8. That is, if one starts with a family of compact CR manifolds embedded in \ mathbb { C } ^ 2, and the CR structure of the family J _ t changes in a real-analytic way with respect to the parameter t, and the CR Yamabe constant of the family of manifolds is uniformly bounded below by a positive constant, then the CR Paneitz operator remains non-negative for the entire family, provided one member of the family has its CR Paneitz operator non-negative.