Differential manifolds provide higher dimensional generalizations of surfaces. They appear in a very natural manner in many areas of mathematics and physics. On a differential manifold or more ...

Harmonic map theory investigates smooth mappings between Riemannian manifolds that minimise or extremise an energy functional. Originating in the mid-twentieth century, it unites techniques from ...

Crystals may seem flawless, but deep inside they contain tiny structural imperfections that dramatically influence their strength and behavior. Researchers from The University of Osaka have used the ...

Application of tools from differential geometry and Lie groups to problems in dynamics, controllability, and motion planning for mechanical systems, particularly with non-Euclidean configuration ...

I work in differential geometry and the application of geometry to the study of partial differential equations. Specifically, my work has focused on conservation laws, Backlund transformations, ...