WebJun 20, 1998 · Abstract. It is an important problem to determine when a complete noncompact Riemannian manifold admits a positive Green's function. In this regard, one tries to seek geometric assumptions which are stable with respect to uniform perturbations of the metric. In this note, we obtained some results in this direction, generalizing some … WebCorollary 2.0.4. Let ! be exact n-form on a compact oriented manifold M of dimension n. Then R M!= 0. Corollary 2.0.5. Let ! be a closed n 1-form on a compact oriented manifold M of dimension n. Then R @M!= 0. Corollary 2.0.6. Let Mn be an oriented manifold. Let ! be a closed k-form on M. Let SˆM be a compact oriented submanifold on M without ...
Aubin
WebFor the Green function, we have the following Theorem: Theorem 1. Suppose a2L1(or C1for simplicity). There exists a unique green function with respect to the di erential operator L as in the above de nition. Moreover, we have the following property: (i) R G … Webwill recover the three big theorems of classical vector calculus: Green’s theorem (for compact 2-submanifolds with boundary in R2), Gauss’ theorem (for compact 3-folds with boundary in R3), and Stokes’ theorem (for oriented compact 2-manifolds with boundary in R3). In the 1-dimensional townpump/contact
Discrete and Continuous Green Energy on Compact Manifolds
WebJan 1, 1982 · I shall prove elsewhere that the condition (0.1) is necessary for the existence of a Green's function for a general connected Riemannian manifold (without any … Webtion of the Green™s function pole™s value on S3 in [HY2], we study Riemannian metric on 3 manifolds with positive scalar and Q curvature. Among other ... Proposition 2.1. Let (M;g) be a smooth compact Riemannian 3 manifold with R>0, Q 0. If u2 C1 (M), u6= constand Pu 0, then u>0 and R u 4g >0. WebTosa tti, Pluricomplex Green’s functions and F ano manifolds 9 N. McCleerey and V. T osatti, Pluricomplex Green’ s functions and Fano manifolds 9 Conversely , given a bounded weakly q ∗ ω FS ,p townpress send