TY  - JOUR
A1  - Bär, Christian
A1  - Hanke, Bernhard
T1  - Local flexibility for open partial differential relations
T2  - Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.
N2  - We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian geometry.
The main application is a general approximation result by sections that have very restrictive local properties on open dense subsets. This shows, for instance, that given any K is an element of Double-struck capital R every manifold of dimension at least 2 carries a complete C-1,C- 1-metric which, on a dense open subset, is smooth with constant sectional curvature K. Of course, this is impossible for C-2-metrics in general.
Y1  - 2021
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/60697
SN  - 0010-3640
SN  - 1097-0312
VL  - 75
IS  - 6
SP  - 1377
EP  - 1415
PB  - Wiley
CY  - Hoboken
ER  -