Integral Formulas and Discrepancy Estimates Using the Fundamental Solution to the Beltrami Operator on Regular Surfaces

The method of equidistribution is sufficiently known for volume integrals over cubes and balls. Moreover, there has been tremendous progress in spherical integration. In this thesis we make the attempt to extend the idea of equidistribution to geoscientifically relevant closed surfaces, such as ellipsoid, spheroid, geoid, and regular real Earth's surface. Essential tool is an integral formula that can be interpreted as the third Green formula on regular surfaces. The main difficulty is the handling of non-sphericity. As particular example an ellipsoid, which is of great significance in Physical Geodesy, is investigated in more detail.