Surface multi-space

Multi-space for curves was defined by Peter Olver to provide geometric foundationsfor symmetry methods in the numerical analysis of ordinary differential equations. Here we define multi-space for surfaces, thereby extending the framework to partial differential equations in two independent variables. The main technical tool is the Hilbert scheme of points on a surface, which we adapt to the context of smooth manifolds. We begin the study of prolongations of group actions, their invariants, and the process of extending a differential equation to multi-space, whereby the resulting equation encompasses both the original differential equation and a family of difference equations approximating it.

Author dc:creator

• Karlsson, Jonas

• Geometry
• Numerical analysis
• Symmetry

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/11299/277369

OAI identifier oai:identifier

oai:conservancy.umn.edu:11299/277369