1. CMB 2011 (vol 55 pp. 632)
|Characterizations of Model Manifolds by Means of Certain Differential Systems|
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. Along the way, we also discover new characterizations of space-forms. We next generalize results concerning metric rigidity via equations involving vector fields.
Keywords:metric rigidity, model manifolds, Obata's type theorems
2. CMB 2011 (vol 55 pp. 487)
|Weighted Model Sets and their Higher Point-Correlations|
Examples of distinct weighted model sets with equal $2,3,4, 5$-point correlations are given.
Keywords:model sets, correlations, diffraction
Categories:52C23, 51P05, 74E15, 60G55
3. CMB 2008 (vol 51 pp. 146)
|Stepping-Stone Model with Circular Brownian Migration |
In this paper we consider the stepping-stone model on a circle with circular Brownian migration. We first point out a connection between Arratia flow on the circle and the marginal distribution of this model. We then give a new representation for the stepping-stone model using Arratia flow and circular coalescing Brownian motion. Such a representation enables us to carry out some explicit computations. In particular, we find the distribution for the first time when there is only one type left across the circle.
Keywords:stepping-stone model, circular coalescing Brownian motion, Arratia flow, duality, entrance law
4. CMB 2001 (vol 44 pp. 459)
|LS-catÃ©gorie algÃ©brique et attachement de cellules |
Nous montrons que la A-cat\'egorie d'un espace simplement connexe de type fini est inf\'erieure ou \'egale \`a $n$ si et seulement si son mod\`ele d'Adams-Hilton est un r\'etracte homotopique d'une alg\`ebre diff\'erentielle \`a $n$ \'etages. Nous en d\'eduisons que l'invariant $\Acat$ augmente au plus de 1 lors de l'attachement d'une cellule \`a un espace. We show that the A-category of a simply connected space of finite type is less than or equal to $n$ if and only if its Adams-Hilton model is a homotopy retract of an $n$-stage differential algebra. We deduce from this that the invariant $\Acat$ increases by at most 1 when a cell is attached to a space.
Keywords:LS-category, strong category, Adams-Hilton models, cell attachments