Local mean value formulas for geometric flow equations
Klaus Ecker
Freie Universitat, Berlin
Mathematics
We will present local monotonicity and mean value formulas for a number of geometric flow equations. The monotonicity formulas establish that an appropriately weighted spacetime portion of energy inside a heat ball (sublevel set a suitably scaled heat kernel) behaves monotonically in the scaling parameter. These formulas are analogous to monotonicity formulas used in geometric variational problems such as for minimal surfaces and harmonic maps.