BV -maps with values into S1: graphs, minimal connections and optimal lifting

H1/2 Maps with Values into the Circle: Minimal Connections, Lifting, and the Ginzburg–landau Equation

On the Stability of Compactified D=11 Supermembranes

We prove D = 11 supermembrane theories wrapping around in an irreducible way over S1×S1×M9 on the target manifold, have a hamiltonian with strict minima and without infinity dimensional valleys for the bosonic sector. The minima occur at monopole connections of an associated U(1) bundle over topologically non trivial Riemann surfaces of arbitrary genus. Explicit expressions for the minimal conn...

Hamilton decompositions of 6-regular Cayley graphs on even Abelian groups with involution-free connections sets

Alspach conjectured that every connected Cayley graph on a finite Abelian group A is Hamiltondecomposable. Liu has shown that for |A| even, if S = {s1, . . . , sk} ⊂ A is an inverse-free strongly minimal generating set of A, then the Cayley graph Cay(A;S?), is decomposable into k Hamilton cycles, where S? denotes the inverse-closure of S. Extending these techniques and restricting to the 6-regu...

Lifting default for S1-valued maps

Let ' 2 C1([0, 1]N ,R). When 0 < s < 1, p 1 and 1  sp < N , the W s,p-semi-norm |'|W s,p of ' is not controlled by |g|W s,p , where g := eı' [3]. [This question is related to existence, for S1-valued maps g, of a lifting ' as smooth as allowed by g.] In [4], the authors suggested that |g|W s,p does control a weaker quantity, namely |'|W s,p+W 1,sp . Existence of such control is due to J. Bourg...

Sobolev maps on manifolds: degree, approximation, lifting

In this paper, we review some basic topological properties of the space X = W s,p(M ;N), where M and N are compact Riemannian manifold without boundary. More specifically, we discuss the following questions: can one define a degree for maps in X? are smooth or not-farfrom-being-smooth maps dense in X? can one lift S1-valued maps?