Research being undertaken by our current postgraduates:
Philip Schrader
Thesis
Riemannian Cubics, Interpolation and Global Analysis
Summary
My research will address the existence of solutions to various interpolation problems on Riemannian manifolds using the techniques of critical point theory and global analysis. These techniques give sufficient conditions for existence of interpolants as well as lower bounds on their multiplicities, whereas previous work has been mainly focused on necessary conditions. Of particular interest are problems where the interpolants are Riemannian cubics or related curves. Such curves are natural choices when a high order of differentiability is required.
Why my research is important
Interpolation problems on Riemannian manifolds arise, for example, in computer graphics and trajectory planning for rigid bodies.
Establishing the existence of solutions is an important step towards applying Riemannian cubics and related curves to these problems.
Statistics clinic
Assistance in statistics is available for Postgraduates students by research at the UWA Centre for Applied Statistics.
University information
CRICOS Code: 00126G
