Nonnegatively curved hypersurfaces with free boundary on a sphere
نویسندگان
چکیده
منابع مشابه
TOPOLOGY OF NONNEGATIVELY CURVED HYPERSURFACES WITH PRESCRIBED BOUNDARY IN Rn
We prove that a smooth compact immersed submanifold of codimension 2 in R, n ≥ 3, bounds at most finitely many topologically distinct compact nonnegatively curved hypersurfaces. Analogous results for noncompact fillings are obtained as well. On the other hand, we show that these topological finiteness theorems may not hold if the prescribed boundary is not sufficiently regular, e.g., C. In part...
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The classical Bernstein Theorem asserts that an entire minimal graph in R must be planar. This theorem was subsequently generalized to higher dimensions by the works of Fleming [10], Almgren [1], DeGiorgi [6], and Simons [23]. The final result states that an entire n-dimensional minimal graph in R must be given by a linear function over R providing that n ≤ 7. On the other hand, nonlinear entir...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2019
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-019-1532-1