Metrics on manifolds with convex or concave boundary. (English) Zbl 0822.53024

Hass, Joel

Gordon, Cameron (ed.) et al., Geometric topology. Joint US-Israel workshop on geometric topology, June 10-16, 1992, Technion, Haifa, Israel. Providence, RI: American Mathematical Society. Contemp. Math. 164, 41-46 (1994).

This paper summarizes the known restrictions on the topology of a 2- or 3-dimensional smooth manifold \(M\) with nonempty boundary, that are imposed by assuming that \(M\) carries a metric of positive or negative curvature and strictly convex or concave boundary. A theorem announced here has since appeared [the author, J. Differ. Geom. 40, No. 3, 449-459 (1994; Zbl 0821.53035)].
For the entire collection see [Zbl 0794.00024].

Reviewer: S.B.Alexander (Urbana)

MSC:

53C20	Global Riemannian geometry, including pinching
57M50	General geometric structures on low-dimensional manifolds
57M35	Dehn’s lemma, sphere theorem, loop theorem, asphericity (MSC2010)

Keywords:

manifold with boundary; metric of positive or negative curvature; convex or concave boundary

Citations:

Zbl 0821.53035