The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ d...The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.展开更多
基金supported by a grant from the Research Grants Council of the Hong Kong Special Administration Region,China(Nos.9041637,CiyuU100711)
文摘The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.
