1,721,065 research outputs found
Convex isoperimetric sets in the Heisenberg group
Full text linkWe characterize convex isoperimetric sets in the Heisenberg group.
We first prove Sobolev regularity for a certain class of R2 -valued vector fields
of bounded variation in the plane related to the curvature equations. Then we
show that the boundary of convex isoperimetric sets is foliated by geodesics of
the Carnot-Caratheodory distance
Heisenberg isoperimetric problem. The axial case.
Full text linkWe prove Pansu’s conjecture about the Heisenberg isoperimetric problem in the
class of axially symmetric sets. The result is based on a weighted rearrangement scheme in the
half plane which is of independent interest
Lipschitz approximation of H-perimeter minimizing boundaries
Full text linkWe prove that the boundary of H-perimeter minimizing sets in
the Heisenberg group can be approximated by graphs that are
intrinsic Lipschitz. The Hausdorff measure of the symmetric
difference in a ball of graph and boundary is estimated
by excess in a larger concentric ball.
This result is motivated by a research program
on the regularity of H-perimeter
minimizing sets
Rearrangements in metric spaces and in the Heisenberg group
Full text linkWe prove several rearrangement theorems in the setting
of a metric measure space. We adapt the general scheme of the argument to the Heisenberg group, where we study
Steiner and circular rearrangement for functions
and sets having a suitable symmetry
Sobolev inequalities for weighted gradients
No full textWe study symmetry, existence, and uniqueness properties of extremal functions for
a weighted Sobolev inequalit
Regularity results for sub-Riemannian geodesics
No full textWe study length minimality of abnormal curves in rank 2 sub-Rieman\-nian
manifolds of polynomial type. As a corollary, we prove a
regularity result for Carnot-Carath\'eodory geode\-sics in a class of rank 2
Carnot groups
Improved Lipschitz approximation of H-perimeter minimizing boundaries
No full textWe prove two new approximation results of H-perimeter minimizing boundaries by means of intrinsic Lipschitz functions in the setting of the Heisenberg group Hn with n≥2. The first one is an improvement of [19] and is the natural reformulation in Hn of the classical Lipschitz approximation in Rn. The second one is an adaptation of the approximation via maximal function developed by De Lellis and Spadaro [11]
A family of nonminimizing abnormal curves
Full text linkIn a four dimensional sub-Riemannian structure, we study
a specific family of abnormal extremals and we show that
they are not length minimizing, answering in the negative
to a question that was recently asked.
We extend the result to a class of 4-dimensional sub-Riemannian
manifolds of step 5
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