Welcome to Shengwen's website!
shengwen.wang at qmul.ac.uk
Queen Mary University of London, School of Mathematical Sciences
Math 371 Ordinary differential equations 2018 Fall, Binghamton University
Math 590F Topics in Analysis 2019 Spring, Binghamton University
Math 371 Ordinary differential equations 2019 Spring, Binghamton University
LTCC course Introduction to mean curvature flow 2020 Fall, London (online)
MA4C0 Differential Geometry 2021 Fall, University of Warwick
MTH 6151 Partial Differential Equations 2022 Fall, Queen Mary University of London
MTH 6151 Partial Differential Equations 2023 Fall, Queen Mary University of London
Geometric analysis and geometric PDEs. I am interested in understanding the formation of singularities and developing/improving regularity theory of geometric partial differential equations such as minimal surfaces, mean curvature flows, Allen-Cahn and Ginzburg-Landau equations, etc.
Publications and preprints:
Round spheres are Hausdorff stable under small perturbation of entropy.
J. Reine Angew. Math. 758, 261-280 (2020). [Link]
On the topological rigidity of self shrinkers in R^3. (with Alexander Mramor)
Int. Math. Res. Not. 2020, 1933-1941 (2020). [Link]
The level set flow of a hypersurface in R^4 of low entropy does not disconnect. (with Jacob Bernstein)
To appear in Comm. Anal. Geom. [Link]
Warped tori with almost non-negative scalar curvature. (with Brian Allen, Lisandra Hernandez-Vazquez, Davide Parise, Alec Payne)
Geometriae Dedicata 200, 153-171 (2019). [Link]
Integrability of scalar curvature and normal metric on conformally flat manifolds. (with Yi Wang)
J. Differential Equations 265, 1353-1370 (2018). [Link]
Low entropy and the mean curvature flow with surgery. (with Alexander Mramor)
To appear in Calc. Var. Partial Differential Equations. [Link]
Extended abstract "The level set flow of a hypersurface in R^4 of low entropy does not disconnect" in the Proceedings of the John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville, May 29 - June 1, 2018 (edited by Theodora Bourni and Mat Langford).
De Gruyter Proc. Math. (2020). [Link]
Precise asymptotics near a pinched disk singularity formed by mean curvature flow. (with Gang Zhou)
Second order estimates for transition layers and a curvature estimate for the parabolic Allen-Cahn. (with Huy Nguyen)
Brakke regularity for the Allen-Cahn flow. (with Huy Nguyen)
Quantization of the energy for the inhomogeneous Allen-Cahn mean curvature. (with Huy Nguyen)