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A remark on a curvature gap for minimal surfaces in the ball
Ezequiel Barbosa, Celso Viana
We extend to higher codimension earlier characterization of the equatorial disk and the critical catenoid by a pinching condition on the length of their second fundamental form amo…
Area rigidity for the equatorial disk in the ball
Ezequiel Barbosa, Celso Viana
It is proved by Brendle in [4] that the equatorial disk has least area among -dimensional free boundary minimal surfaces in the Euclidean ball . By comparing the exce…
Index one minimal surfaces in spherical space forms
Celso Viana
We prove that orientable index one minimal surfaces in spherical space forms with large fundamental group have genus at most two. This confirms a conjecture of R. Schoen for an inf…
A note on the evolution of the Whitney sphere along mean curvature flow
Celso Viana
We study the evolution of the Whitney sphere along the Lagrangian mean curvature flow. We show that equivariant Lagrangian spheres in satisfying mild geometric assum…