Heatball localizations of monotone functionals on evolving manifolds

Topic

Monotone functionals give important information for the analysis of
geometric evolution equations. I will describe a quite general
mechanism for localizing such functionals. This construction results in
what may be regarded as local mean-value, monotonicity, or Lyapunov
formulas. In particular, the construction yields a purely local
monotone quantity directly analogous to Perelman's reduced volume for
Ricci flow, and another related to Perelman's average energy. This is
joint work with Klaus Ecker, Lei Ni, and Peter Topping.