The Willmore Conjecture for immersed tori with small curvature integral
نویسنده
چکیده
The Willmore conjecture states that any immersion F : T 2 → Rn of a 2-torus into euclidean space satisfies ∫ T 2 H 2 ≥ 2π2. We prove it under the condition that the Lp-norm of the Gaussian curvature is sufficiently small.
منابع مشابه
The Willmore Conjecture in the Real Projective Space
-We prove that for any torus M immersed in the real projective space RP(1) with mean curvature H, we have that ∫ M (1 +H )dA ≥ π and that the equality holds only for the minimal Clifford torus. In terms of the three sphere, this result says that the Willmore conjecture is true for immersed tori in S(1) invariant under the antipodal map. Mathematics Subject Classification: 53A10, 53A05, 53C42.
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