论文标题
toponogov猜想在完整表面上的证明
Proof of the Toponogov Conjecture on Complete Surfaces
论文作者
论文摘要
我们证明了在完整凸面上的toponogov的猜想，即这种平面必须包含一个脐带，尽管在无穷大。我们的证明是间接的。它使用相关的Riemann-Hilbert边界价值问题的Fredholm规律性，以及具有拉格朗日边界条件的Holomorthic Discs的存在结果，两者都适用于推定的反例。 主要定理的推论包括鹰派奇异型定理，以及在凸案例中从1965年开始对米尔诺的猜想的证明。
We prove a conjecture of Toponogov on complete convex planes, namely that such planes must contain an umbilic point, albeit at infinity. Our proof is indirect. It uses Fredholm regularity of an associated Riemann-Hilbert boundary value problem and an existence result for holomorphic discs with Lagrangian boundary conditions, both of which apply to a putative counterexample. Corollaries of the main theorem include a Hawking-Penrose singularity-type theorem, as well as the proof of a conjecture of Milnor's from 1965 in the convex case.
