Geometry of Partial Differential Equations
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, intermediate equations, and sub-Finsler geometry with applications to control theory.
- Geometry of conservation laws for a class of parabolic partial differential equations, Selecta Math. (New Series) 3 (1997) 1-77.
- Geometry of conservation laws for a class of parabolic PDEs II: Normal forms for equations with conservation laws. Selecta Math. (New Series). 3 (1997) 497-515.
- Homogeneous Backlund transformations of hyperbolic Monge-Ampere systems. Asian J. Math. 6 (2002) 433-480.}
- Parametric Backlund transformations I: Phenomenology, (with T. Ivey). Trans. Amer. Math. Soc. 357 (2005) 1061-1093.
- Sub-Finsler geometry in dimension three, (with C. G. Moseley). Differential Geometry Appl. 24 (2006) 628-651.