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    Scientists / Open questions

    陈省身

    Shiing-Shen Chern

    微分几何、示性类

    9 个问题

    1. Dropping the Gauss-map degree hypothesis from Chern–Lashof's Theorem 4: convexity of closed hypersurfaces with sign-constant Gauss–Kronecker curvature

    2. Optimal Heinz-type radius bounds for graphs with negative scalar curvature (Chern's 1965 estimate for σ2≤−c\sigma_2\le -c)

    3. Local classification of proper Dupin hypersurfaces in EnE^n for n≥5n \geq 5 up to Lie sphere equivalence

    4. Classification of maximal-rank webs at the exceptional value d=(r+2)(n−1)+1d=(r+2)(n-1)+1 with n≥3n\geq 3, and the existence of non-grassmannian maximal-rank webs below the extremal range q(d)≥n−1q(d)\geq n-1

    5. Finite-order termination of the local equivalence problem for multidimensional 3-webs (Chern, 1935)

    6. Cohomological relation between the tangent and normal Gauss maps of a submanifold of Euclidean space

    7. Canonical selection among, and degenerate extension of, Chern's family of Euclidean connections in Finsler spaces

    8. The Chern-Goldberg volume-decreasing problem for real harmonic maps: the sign of the invariant CC and the removal of the hypothesis C≤0C \le 0

    9. Hopf's problem on the rigidity and classification of constant-mean-curvature spheres beyond the classical setting: higher-dimensional space forms and higher genus

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