# Ling Xiao

Hill Assistant Professor

Department of Mathematics, Rutgers University

Email : lx70(at)math.rutgers.edu

Office : Hill 342

I completed my Ph.D. at Johns Hopkins University in 2013, under the supervision of Prof. Joel Spruck. Right now, I'm a Hill Assistant Professor at Rutgers University. In Fall 2013, I was at MSRI, for the program in Optimal Transport: Geometry and Dynamics. After that, I spent a semester at Cornell University.

I am interested in partial differential equation, geometric analysis, and geometric measure theorem.

## Papers

1. Interior curvature estimates and the asymptotic plateau problem in hyperbolic space, (joint with Bo Guan and Joel Spruck), J. Differential Geom. 96 (2014), no. 2, 201–222.

2. Curvature flow of complete hypersurfaces in hyperbolic space, Geom. Dedicata 164 (2013), 357–383.

3. Modified mean curvature flow of star-shaped hypersurfaces in hyperbolic space, (joint with Longzhi Lin), Comm. Anal. Geom. 20 (2012), no. 5, 1061–1096.

4. Convex spacelike hypersurfaces of constant curvature in de Sitter space, (joint with Joel Spruck ), Discrete Contin. Dyn. Syst. Ser. B 17 (2012), no. 6, 2225–2242.

5. Curvature flow of complete convex hypersurfaces in hyperbolic space, J. Geom. Anal. 23 (2013), no. 4, 1641–1673.

6. The Weyl problem with nonnegative Gauss curvature in hyperbolic space, (joint with Jui-En Chang), Canad. J. Math. 67 (2015), no. 1, 107–131.

7. Entire downward translating solitons to the mean curvature flow in Minkowski space, (joint with Joel Spruck), Proc. Amer. Math. Soc. 144 (2016), no. 8, 3517–3526.

8. Gradient estimates and lower bound for the blow-up time of star-shaped mean curvature flow .

9. Minimal Graphs and Graphical Mean Curvature Flow in $M \times \mathbb R$ , (joint with Matthew McGonagle).

10. A note on starshaped compact hypersurfaces with a prescribed scalar curvature in space forms , (joint with Joel Spruck), to appear in Revista Matemática Iberoamericana.

11. Motion of level set by general curvature .

12. General curvature flow without singularities .

13. Neumann boundary value problem for general curvature flow with forcing term .

14. Complete translating solitons to the mean curvature flow in $\mathbb{R}^3$ with nonnegative mean curvature , (joint with Joel Spruck).

15. Infinite boundary value problem for translating solitons , (joint with Joel Spruck).