In this short note we extend Hamilton’s advanced maximum principle for parabolic systems on closed manifolds to the case of manifolds with boundary, which also generalizes a Hopf type theorem of Shen.

We study natural families of ∂-operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulæ for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expressed in terms of the Chern characters of natural vector bundles related to the parabo...

A recent result of Kalton and Weis is extended to the case of noncommuting operators, employing the commutator condition of Labbas and Terreni, or of Da Prato and Grisvard. Under appropriate assumptions it is shown that the sum of two non-commuting operators admits an H∞-calculus. The main results are then applied to a parabolic problem on a wedge domain.

We describe all real points of the parameter space of two-generator Kleinian groups with a parabolic generator, that is, we describe a certain twodimensional slice through this space. In order to do this we gather together known discreteness criteria for two-generator groups and present them in the form of conditions on parameters. We complete the description by giving discreteness criteria for...

By means of energy and entropy estimates, we prove existence and positivity results in higher space dimensions for degenerate parabolic equations of fourth order with nonnegative initial values. We discuss their asymptotic behavior for t → ∞ and give a counterexample to uniqueness.

How does one determine a surface which is as flat as possible, such as those created by soap film surfaces? What does it mean to be as flat as possible? In this paper we address this question from two distinct points of view, one local and one global in nature. Continuing with this theme, we put a temporal twist on the question and ask how to evolve a surface so as to flatten it as efficiently ...

Skew product semiflow Πt : X × Y → X × Y which is generated by