A Gap Theorem for Willmore Tori and an Application to the Willmore Flow
نویسنده
چکیده
In 1965 Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R3 is at least 2π2 and attains this minimal value if and only if the torus is a Möbius transform of the Clifford torus. This was recently proved by Marques and Neves in [13]. In this paper, we show for tori there is a gap to the next critical point of the Willmore energy and we discuss an application to the Willmore flow. We also prove an energy gap from the Clifford torus to surfaces of higher genus.
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