STEIN EMBEDDING THEOREM FOR $\mathbb{B}$-MANIFOLDS

A proof of Sobolev’s Embedding Theorem for Compact Riemannian Manifolds

Observe that H 0 (M) = L p(M). Also, Hk := H2 k is a Hilbert space under the L2-inner product. F k contains only smooth functions. In general, a sequence in F k will not converge in the H k norm to a function in F k , so we need to complete the space to have anything useful. An alternate approach would have been to start with functions in Lp rather than completing the space of smooth functions ...

Plateau–Stein Manifolds

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 hypersurfac...

Holomorphic Submersions from Stein Manifolds

Holomorphic Submersions from Stein Manifolds

Lagrangian isotopies in Stein manifolds

Studying the space of Lagrangian submanifolds is a fundamental problem in symplectic topology. Lagrangian spheres appear naturally in the Leftschetz pencil picture of symplectic manifolds. In this paper we demonstrate the uniqueness up to Hamiltonian isotopy of the Lagrangian spheres in some 4-dimensional Stein symplectic manifolds. The most important example is the cotangent bundle of the 2-sp...