| Abstract: |
| We consider the classical geometric problem of prescribing scalar and
boundary mean curvature via conformal deformation of the metric on a
n-dimensional compact Riemannian manifold. We deal with the case of
negative scalar curvature and positive boundary mean curvature. It is
known that if n=3 all the blow-up points are isolated and simple. In
this work we prove that this is not true anymore in low dimensions (that
is n=4, 5, 6, 7).
In particular, we construct a solution with a clustering blow-up
boundary point (i.e. non-isolated), which is non-umbilic and
minimizes the norm of the trace-free second fundamental form of the
boundary. |
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