Anne Meyers Cohler

To Anne

Anne O’Tate

Anne Magurran

The overwhelming appeal of the concept of evolution through natural selection has focused the minds of generations of biologists on trends, and the similarities and differences between organisms that is grist to the mill of taxonomists. “To paraphrase T.S. Eliot, ‘Where is the imagination that has been lost in knowledge and where is the knowledge that has been lost in information?’ This book is...

A Note on Meyers’ Theorem in W

Lower semicontinuity properties of multiple integrals u ∈W (Ω;R) 7→ ∫ Ω f(x, u(x), · · · ,∇u(x)) dx are studied when f may grow linearly with respect to the highest-order derivative, ∇ku, and admissible W k,1(Ω;Rd) sequences converge strongly in W k−1,1(Ω;Rd). It is shown that under certain continuity assumptions on f, convexity, 1-quasiconvexity or k-polyconvexity of ξ 7→ f(x0, u(x0), · · · ,∇...

2 Patrick Mcdonald and Robert Meyers

Let M be a complete Riemannian manifold and D ⊂ M a smoothly bounded domain with compact closure. We use Brownian motion and the classic results on the Stieltjes moment problem to study the relationship between the Dirichlet spectrum of D and the heat content asymptotics of D. Central to our investigation is a sequence of invariants associated to D defined using exit time moments. We prove that...