Calculus of Variations and Geometric Measure Theory

D. Mucci

Maps into projective spaces: liquid crystal and conformal energies

created by mucci on 01 Mar 2010
modified on 21 Dec 2011


Published Paper

Inserted: 1 mar 2010
Last Updated: 21 dec 2011

Journal: DCDS-B
Volume: 17
Number: 2
Pages: 597--635
Year: 2012


Variational problems for the liquid crystal energy of mappings from three-dimensional domains into the real projective plane are studied. More generally, we study the dipole problem, the relaxed energy, and density properties concerning the conformal $p$-energy of mappings from $n$-dimensional domains that are constrained to take values into the $p$-dimensional real projective space, for any positive integer $p$. Furthermore, a notion of optimally connecting measure for the singular set of such class of maps is given.