Publications
Published or Accepted Publications
1. Real analytic solutions to the Willmore flow. Ninth MSU-UAB Conference on Differential Equations
and Computational Simulations; Electron. J. Diff. Eqns., Conf. 20, pp. 151-164 (2013).
2. Continuous maximal regularity on uniformly regular Riemannian manifolds. J. Evol. Equ. 1, no. 14,
211-248 (2014). (With Gieri Simonett)
3. A family of parameter-dependent diffeomorphisms acting on function spaces over a
Riemannian manifold and applications to geometric flows. NoDEA Nonlinear Differential Equations
Appl. 22, no. 1, 45-85 (2015).
4. Some remarks on uniformly regular Riemannian manifolds. Math. Nachr. 289, No. 2-3, 232-242
(2016). (With Marcelo Disconzi, and Gieri Simonett)
5. On the regularity of the interface of a thermodynamically consistent two-phase Stefan problem.
Interfaces Free Bound. 17, no. 4, 555–600 (2015). (With Jan Prüss, and Gieri Simonett)
6. Singular parabolic equations of second order on manifolds with singularities. J. Differential
Equations 260, no. 2, 1747-1800 (2016).
7. Continuous maximal regularity on manifolds with singularities and its applications. Evol. Equ.
and Control Theory 5, no. 2, 303-335 (2016).
8. Wellposedness of a nonlocal nonlinear diffusion equation in image processing. Nonlinear Anal. 150, 114-137 (2017). (With Patrick Guidotti)
Submitted Papers
1. The Yamabe flow on incomplete manifolds. Submitted. arXiv: 1506.07018.
2. Global solutions to the porous medium equations on singular manifolds. Submitted. arXiv:
1606.01233.
Papers in Preparation
1. Instantaneously regularized solutions to parabolic equations with interior degeneracy or
singularity. In preparation. (With Patrick Guidotti)
2. Boundary value problems on singular manifolds. In preparation.
3. Heat flow of harmonic maps with weak anchoring boundary condition in dimension two.
In preparation. (With Tao Huang and Changyou Wang)