Thalia Jeffres, Assistant Professor
Differential Geometry; PhD, SUNY at StonyBrook, 1996
Dr. Jeffres' field of investigation is Riemannian and complex differential geometry. In particular, she is interested in special metrics on manifolds that are noncompact or which have singularities. Special metrics are those for which some curvature is constant. Since the curvature is an expression in the derivatives of the metric, setting this equal to a constant yields a partial differential equation. Therefore, solution of these problems frequently also involves some PDE techniques. Related to this, Dr. Jeffres is also interested in the heat operator.
Miranda Jones (current)
Conformal Deformations of Conic Metrics to Constan Scalar Curvature, Math. Res. Lett., 17 (2010), no. 3, 449-465.
Gauss Curvature Flow on Surfaces of Revolution, Advances in Gometry, 9 (2009), no. 2, 189-197.
Vertical Blow Ups of Capillary Surfaces in R3 Part II: Nonconvex Corners, with Kirk Lancaster, Electron. J. Diff. Eqns. Vol. 2008 (2008), No. 160,1-25.
Vertical Blow Ups of Capillary Surfaces in R3 Part I: Convex Corners, with Kirk Lancaster, Electronic Journal of Differential Equations, Vol. 2007 (2007), No. 152, 1-24.
Maximum Principle for Parabolic Equations on a Manifold with Cone Singularities, Adv. Geom. 5 (2005), 319-323.
Regularity of the Heat Operator on a Manifold with Cylindrical Ends, Pacific J. Math. 215 (2004), no. 2, 331-345.