1,265 research outputs found
On the codimension of the abnormal set in step two Carnot groups
In this article we prove that the codimension of the abnormal set of the
endpoint map for certain classes of Carnot groups of step 2 is at least three.
Our result applies to all step 2 Carnot groups of dimension up to 7 and is a
generalisation of a previous analogous result for step 2 free nilpotent groups
Fine properties of functions with bounded variation in Carnot-Carath\'eodory spaces
We study properties of functions with bounded variation in
Carnot-Ca\-ra\-th\'eo\-do\-ry spaces. We prove their almost everywhere
approximate differentiability and we examine their approximate discontinuity
set and the decomposition of their distributional derivatives. Under an
additional assumption on the space, called property , we show that
almost all approximate discontinuities are of jump type and we study a
representation formula for the jump part of the derivative
Mok's characteristic varieties and the normal holonomy group
In this paper we complete the study of the normal holonomy groups of complex
submanifolds (non nec. complete) of Cn or CPn. We show that irreducible but non
transitive normal holonomies are exactly the Hermitian s-representations of
[CD09, Table 1] (see Corollary 1.1). For each one of them we construct a non
necessarily complete complex submanifold whose normal holonomy is the
prescribed s-representation. We also show that if the submanifold has
irreducible non transitive normal holonomy then it is an open subset of the
smooth part of one of the characteristic varieties studied by N. Mok in his
work about rigidity of locally symmetric spaces. Finally, we prove that if the
action of the normal holonomy group of a projective submanifold is reducible
then the submanifold is an open subset of the smooth part of a so called join,
i.e. the union of the lines joining two projective submanifolds
- …