A compactness result for non-local unregularized gradient flow lines

On local non-compactness in recursive mathematics

A metric space is said to be locally non-compact if every neighborhood contains a sequence that is bounded away from every element of the space, hence contains no accumulation point. We show within recursive mathematics that a nonvoid complete metric space is locally non-compact iff it is without isolated points. The result has an interesting consequence in computable analysis: If a complete me...

A Bifurcation Result for Non-local Fractional Equations

In the present paper we consider problems modeled by the following non-local fractional equation { (−∆)u− λu = μf(x, u) in Ω u = 0 in R \ Ω , where s ∈ (0, 1) is fixed, (−∆) is the fractional Laplace operator, λ and μ are real parameters, Ω is an open bounded subset of R, n > 2s , with Lipschitz boundary and f is a function satisfying suitable regularity and growth conditions. A critical point ...

A compactness result for Landau state in thin-film micromagnetics

Compactness theorems for gradient Ricci solitons

In this paper, we prove the compactness theorem for gradient Ricci solitons. Let (Mα, gα) be a sequence of compact gradient Ricci solitons of dimension n ≥ 4, whose curvatures have uniformly bounded L n 2 norms, whose Ricci curvatures are uniformly bounded from below with uniformly lower bounded volume and with uniformly upper bounded diameter, then there must exists a subsequence (Mα, gα) conv...

A footnote on local compactness

A standard example of an impredicative definition is that of the way-below relation [11], and thus of local compactness in (point-free) topology [6]. Local compactness can be dealt with predicatively as in [8], [5]; the particularly convenient re-formulation to be presented is based on a recent result by Peter Aczel [2], and on the observation that, in set-presented topologies, the way-below re...