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# Geometric Analysis and Partial Differential Equations Seminar

## May 14, 2014 @ 10:30 am - 11:30 pm

##### Speaker

Dr Lashi Bandara (The Australian National University)

##### Title

Rough metrics and quadratic estimates

##### Abstract

A consequence of the Kato square root problem on manifolds is a certain “stability” it provides in terms of perturbation at the level of the metric. This is best examined by considering certain quadratic estimates associated with the problem. Here, I will talk about a class of Riemann-like metrics on manifolds, which are permitted to be both of low regularity and degenerate, under which these quadratic estimates remain invariant. This metric perturbation technique also allows us to capture Lipschitz transformations of spaces in terms of pullback metrics. Furthermore, we use the perturbation mechanism to show that the Kato square root problem can be solved for metrics with zero injectivity radius bounds.