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A geometric approach to on-diagonal heat kernel lower bounds on groups

Thierry Coulhon, Alexander Grigor'yan, Christophe Pittet (2001)

Annales de l’institut Fourier

We introduce a new method for obtaining heat kernel on-diagonal lower bounds on non- compact Lie groups and on infinite discrete groups. By using this method, we are able to recover the previously known results for unimodular amenable Lie groups as well as for certain classes of discrete groups including the polycyclic groups, and to give them a geometric interpretation. We also obtain new results for some discrete groups which admit the structure of a semi-direct product or of a wreath product....

A geometric approach to universal quasigroup identities

Václav J. Havel (1993)

Archivum Mathematicum

In the present paper we construct the accompanying identity I ^ of a given quasigroup identity I . After that we deduce the main result: I is isotopically invariant (i.e., for every guasigroup Q it holds that if I is satisfied in Q then I is satisfied in every quasigroup isotopic to Q ) if and only if it is equivalent to I ^ (i.e., for every quasigroup Q it holds that in Q either I , I ^ are both satisfied or both not).

A geometric description of Hazama's exceptional classes

Federica Galluzzi (2000)

Bollettino dell'Unione Matematica Italiana

Sia X una varietà abeliana complessa di tipo Mumford. In queste note daremo una descrizione esplicita delle classi eccezionali in B 2 X × X trovate da Hazama in [Ha] e le descriveremo geometricamente usando la grassmaniana delle rette di P 7 .

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