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math.DG2026
Local Convexity and Planarity Estimates for Mean Curvature Flow
Liang Cheng
We establish local convexity and cylindrical pinching estimates for hypersurface mean curvature flow under an intermediate convexity condition and integral bounds on the mean curva…
math.DG2026
On Positively Curved Einstein Four-Manifolds with Euler Characteristic at Most Three
Liang Cheng
It is conjectured that a complete, orientable Einstein four-manifold with strictly positive sectional curvature must be isometric to either the round four-sphere or the compl…
math.AP2026
Ball and Spherical-Shell Rigidity from Overdetermined Translating Solitons
Liang Cheng, Li Ma
We study overdetermined boundary problems for the graphical translating-soliton equation \[ -\operatorname{div}\!\left(\frac{Du}{\sqrt{1+|Du|^2}}\right) =\frac{1}{\sqrt{1+|Du|^2}}…