  We extend field patching to the setting of Berkovich analytic geometry and
use it to prove a local-global principle over function fields of analytic
curves. We apply this result to quadratic forms, and combine it with sufficient
conditions for local isotropy over a Berkovich curve to obtain applications on
the u-invariant. The patching method we adapt was introduced by Harbater and
Hartmann, and further developed by these two authors and Krashen. This paper
generalizes their results on the local-global principle and quadratic forms.
