New mathematical theory for fluid motion on surfaces with holes.

There are very few explicit results in a fundamental mathematical theory on complicated curved surfaces, such as those with holes. There are, however, many explicit results in this theory on simpler curved surfaces, such as the sphere. This project aims to develop new explicit results in this important mathematical theory on surfaces with holes. Owing to the geometrical properties of these surfaces, and the explicit form the new results shall have, the outcomes from this project should be of great theoretical importance, providing a toolbox for solving many different mathematical problems on curved surfaces. The new results should also have application to the analysis of fluid flows over porous media and practical engineering structures.