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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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Conformal changes of metric and geodesics
In "A foliation of geodesics is characterized by having no “tangent homologies”, J. of Pure and Applied Algebra Volume 13, Issue 1, 1978, Pages 101–104 D. Sullivan explains a necessary and sufficient …