Plateau–Stein Manifolds
نویسنده
چکیده
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f . We show, for instance, that if an X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.
منابع مشابه
Holomorphic Functions of Slow Growth on Coverings of Pseudoconvex Domains in Stein Manifolds
We apply the methods developed in [Br1] to study holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds. In particular, we extend and strengthen certain results of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds in the case of coverings of Stein manifolds.
متن کاملA note on Stein fillings of contact manifolds
We construct infinitely many distinct simply connected Stein fillings of a certain infinite family of contact 3-manifolds. Math. Res. Lett. 15 (2008), no. 6, 1127–1132 c © International Press 2008 A NOTE ON STEIN FILLINGS OF CONTACT MANIFOLDS Anar Akhmedov, John B. Etnyre, Thomas E. Mark, and Ivan Smith Abstract. In this note we construct infinitely many distinct simply connected Stein fillings...
متن کاملHartogs Type Theorems on Coverings of Stein Manifolds
We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of Stein manifolds.
متن کاملStein Domains and Branched Shadows of 4-manifolds
We provide sufficient conditions assuring that a suitably decorated 2-polyhedron can be thickened to a compact 4-dimensional Stein domain. We also study a class of flat polyhedra in 4-manifolds and find conditions assuring that they admit Stein, compact neighborhoods. We base our calculations on Turaev’s shadows suitably “smoothed”; the conditions we find are purely algebraic and combinatorial.
متن کاملAn Invariant of Smooth 4–Manifolds
We define a diffeomorphism invariant of smooth 4–manifolds which we can estimate for many smoothings of R and other smooth 4–manifolds. Using this invariant we can show that uncountably many smoothings of R support no Stein structure. Gompf [11] constructed uncountably many smoothings of R which do support Stein structures. Other applications of this invariant are given. AMS Classification numb...
متن کامل