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.

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.
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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.
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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.
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5.
Curvature flow of complete convex hypersurfaces in hyperbolic space,
J. Geom. Anal. 23 (2013), no. 4, 1641–1673.
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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.
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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.
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8.
Gradient estimates and lower bound for the blow-up time of star-shaped mean curvature flow .
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9.
Minimal Graphs and Graphical Mean Curvature Flow in $M \times \mathbb R$ ,
(joint with Matthew McGonagle).
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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.
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11.
Motion of level set by general curvature .
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12.
General curvature flow without singularities .
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13.
Neumann boundary value problem for general curvature flow with forcing term .
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14.
Complete translating solitons to the mean curvature flow in $\mathbb{R}^3$ with nonnegative mean curvature ,
(joint with Joel Spruck).
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15.
Infinite boundary value problem for translating solitons ,
(joint with Joel Spruck).
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