Relative Yamabe Invariant

Details Relative Yamabe Invariant Relative Yamabe Invariant

2000-08-17

arxiv.org/abs/math/0008138v1

Mathematics

Differential Geometry

24 pages, 5 fig

Scientific paper

We define a relative Yamabe invariant of a smooth manifold with given conformal class on its boundary. In the case of empty boundary the invariant coincides with the classic Yamabe invariant. We develop approximation technique which leads to gluing theorems of two manifolds along their boundaries for the relative Yamabe invariant. We show that there are many examples of manifolds with both positive and non-positive relative Yamabe invariants.

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