821 research outputs found
The Construction of Doubly Periodic Minimal Surfaces via Balance Equations
Using Traizet’s regeneration method, we prove the existence of many new 3-dimensional families of embedded, doubly periodic minimal surfaces. All these families have a foliation of R3 by vertical planes as a limit. In the quotient, these limits can be realized conformally as noded Riemann surfaces, whose components are copies of C∗ with finitely many nodes. We derive the balance equations for the location of the nodes and exhibit solutions that allow for surfaces of arbitrarily large genus and number of ends in the quotient
Lowering topological entropy over subsets revisited
Let be a topological dynamical system. Denote by and the covering entropy and dimensional entropy of ,
respectively. is called D-{\it lowerable} (resp. {\it lowerable}) if
for each there is a subset (resp. closed subset)
with (resp. ); is called D-{\it hereditarily
lowerable} (resp. {\it hereditarily lowerable}) if each Souslin subset (resp.
closed subset) is D-lowerable (resp. lowerable).
In this paper it is proved that each topological dynamical system is not only
lowerable but also D-lowerable, and each asymptotically -expansive system is
D-hereditarily lowerable. A minimal system which is lowerable and not
hereditarily lowerable is demonstrated.Comment: All comments are welcome. Transactions of the American Mathematical
Society, to appea
Realising end invariants by limits of minimally parabolic, geometrically finite groups
We shall show that for a given homeomorphism type and a set of end invariants
(including the parabolic locus) with necessary topological conditions which a
topologically tame Kleinian group with that homeomorphism type must satisfy,
there is an algebraic limit of minimally parabolic, geometrically finite
Kleinian groups which has exactly that homeomorphism type and end invariants.
This shows that the Bers-Sullivan-Thurston density conjecture follows from
Marden's conjecture proved by Agol, Calegari-Gabai combined with Thurston's
uniformisation theorem and the ending lamination conjecture proved by Minsky,
partially collaborating with Masur, Brock and Canary.Comment: fourth version: Introduction rewritten; some arguments in Sec. 5 and
6 clarified
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