Yueh-Ju Lin, Assistant Professor

Mathematics, PhD, University of Notre Dame, 2014




Yueh-Ju Lin works in Geometric Analysis and Differential Geometry. More precisely, she is interested in nonlinear elliptic partial differential equations (PDEs) arising in conformal geometry. Such equations appear naturally when looking for better behaved metrics within a conformal class. A number of her research problems focus on quadratic curvature functionals in conformal geometry, which lead to the question of the solvability of fourth-order elliptic PDEs. The higher order curvature quantity she is interested in, is a higher-order analogue of Gaussian curvature and scalar curvature. She is also interested in studying classification, stability and rigidity phenomena for higher order curvatures or general conformally variational invariants.


Selected Publications:

  • (with W. Yuan) Deformations of Q - Curvature I, Calc. Var. Partial Differential Equations 55 (2016), no. 4, Paper No. 101, 29 pp.
  • (with M. Gursky, F. Hang) Riemannian manifolds with positive Yamabe invariant and Paneitz operator, Int. Math. Res. Not. IMRN 2016, no. 5, 1348 - 1367.
  • Connected sum construction of constant Q curvature manifolds in higher dimensions, Differential Geom. Appl. 40 (2015), 290 - 320.