Siyuan Lu
Associate Professor
Associate Professor
Department of Mathematics and Statistics
Department of Mathematics and Statistics
McMaster University
McMaster University
Hamilton Hall
Hamilton Hall
1280 Main Street West, Hamilton, ON, L8S 4K1
1280 Main Street West, Hamilton, ON, L8S 4K1
Telephone: 905-525-9140 ext. 23627
Telephone: 905-525-9140 ext. 23627
Email: siyuan.lu@mcmaster.ca
Email: siyuan.lu@mcmaster.ca
Research Interests: Geometric Analysis, Partial Differential Equations, Geometric Flows and General Relativity.
Research Interests: Geometric Analysis, Partial Differential Equations, Geometric Flows and General Relativity.
Publications:
Publications:
15. S. Lu, Interior C^2 estimate for Hessian quotient equation in general dimension,
15. S. Lu, Interior C^2 estimate for Hessian quotient equation in general dimension,
arXiv: 2401.12229.
arXiv: 2401.12229.
14. S. Lu, Interior C^2 estimate for Hessian quotient equation in dimension three,
14. S. Lu, Interior C^2 estimate for Hessian quotient equation in dimension three,
arXiv: 2311.05835.
arXiv: 2311.05835.
13. S. Lu, Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space,
13. S. Lu, Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space,
Calc. Var. Partial Differential Equations 62 (2023), no. 9, Paper No. 257.
Calc. Var. Partial Differential Equations 62 (2023), no. 9, Paper No. 257.
12. S. Lu, On the asymptotic Plateau problem in hyperbolic space,
12. S. Lu, On the asymptotic Plateau problem in hyperbolic space,
Proc. Amer. Math. Soc. 151 (2023), no. 12, 5443-5451.
Proc. Amer. Math. Soc. 151 (2023), no. 12, 5443-5451.
11. Y.Y. Li, H. Lu and S. Lu, A Liouville theorem for Mobius invariant equations,
11. Y.Y. Li, H. Lu and S. Lu, A Liouville theorem for Mobius invariant equations,
Peking Math. J. 6 (2023), no. 2, 609-634.
Peking Math. J. 6 (2023), no. 2, 609-634.
10. S. Lu, On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase,
10. S. Lu, On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase,
Discrete Contin. Dyn. Syst. 43 (2023), no. 7, 2561-2575.
Discrete Contin. Dyn. Syst. 43 (2023), no. 7, 2561-2575.
9. Y.Y. Li and S. Lu, Monge-Ampere equation with bounded periodic data,
9. Y.Y. Li and S. Lu, Monge-Ampere equation with bounded periodic data,
Anal. Theory Appl. 38 (2022), no. 2, 128-147.
Anal. Theory Appl. 38 (2022), no. 2, 128-147.
8. Y.Y. Li, H. Lu and S. Lu, On the \sigma_2-Nirenberg problem on \mathbb{S}^2,
8. Y.Y. Li, H. Lu and S. Lu, On the \sigma_2-Nirenberg problem on \mathbb{S}^2,
J. Funct. Anal. 283 (2022), no. 10, Paper No. 109606, 50pp.
J. Funct. Anal. 283 (2022), no. 10, Paper No. 109606, 50pp.
7. S. Lu and P. Miao, Rigidity of Riemannian Penrose inequality with corners and its implications,
7. S. Lu and P. Miao, Rigidity of Riemannian Penrose inequality with corners and its implications,
J. Funct. Anal. 281 (2021) no. 10, Paper No. 109231, 11pp.
J. Funct. Anal. 281 (2021) no. 10, Paper No. 109231, 11pp.
6. S. Lu, On Weyl’s embedding problem in Riemannian manifolds,
6. S. Lu, On Weyl’s embedding problem in Riemannian manifolds,
Int. Math. Res. Not. IMRN 2020, no. 11, 3229-3259.
Int. Math. Res. Not. IMRN 2020, no. 11, 3229-3259.
5. S. Lu and P. Miao, Variation and rigidity of quasi-local mass,
5. S. Lu and P. Miao, Variation and rigidity of quasi-local mass,
Adv. Theor. Math. Phys. 23 (2019), no. 5, 1411-1426.
Adv. Theor. Math. Phys. 23 (2019), no. 5, 1411-1426.
4. S. Lu and P. Miao, Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature,
4. S. Lu and P. Miao, Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature,
J. Differential Geom. 113 (2019), no. 3, 519-566.
J. Differential Geom. 113 (2019), no. 3, 519-566.
3. S. Lu, Inverse curvature flow in anti-de Sitter-Schwarzschild manifold
3. S. Lu, Inverse curvature flow in anti-de Sitter-Schwarzschild manifold
Comm. Anal. Geom. 27 (2019), no. 2, 465-489.
Comm. Anal. Geom. 27 (2019), no. 2, 465-489.
2. Y.Y. Li and S. Lu, Existence and nonexistence to exterior Dirichlet problem for Monge-Ampere equation,
2. Y.Y. Li and S. Lu, Existence and nonexistence to exterior Dirichlet problem for Monge-Ampere equation,
Calc. Var. Partial Differential Equations 57 (2018), no. 6, Art.161, 17 pp.
Calc. Var. Partial Differential Equations 57 (2018), no. 6, Art.161, 17 pp.
1. P. Guan and S. Lu, Curvature estimates for immersed hypersurfaces in Riemannian manifolds,
1. P. Guan and S. Lu, Curvature estimates for immersed hypersurfaces in Riemannian manifolds,
Invent. Math. 208 (2017), no. 1, 191-215.
Invent. Math. 208 (2017), no. 1, 191-215.
Supervision:
Supervision:
1. Bin Wang: (M. Sc. McMaster University 2022)
1. Bin Wang: (M. Sc. McMaster University 2022)
B. Wang, Curvature estimates for hypersurfaces of constant curvature in hyperbolic space,
B. Wang, Curvature estimates for hypersurfaces of constant curvature in hyperbolic space,
to appear in Math. Res. Lett.
to appear in Math. Res. Lett.