Commit 614a0bac authored by Felix Hilsky's avatar Felix Hilsky
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add question, citation

parent 842cb814
......@@ -40,7 +40,6 @@ He therefore coined the term \newTerm{flüssiger Kristall}, in English \newTerm{
\label{fig:schlieren}
\end{figure}
In a liquid crystal the molecules agree locally on their direction.
In some liquid crystals there is also a partial ordering in the position of the molecules.
Otherwise they are positioned isotropically.
......@@ -188,9 +187,10 @@ and surfaces (two-dimensional domains) (\cref{sec:sobolev_orientability_on_surfa
For flat domains the presented problems were discussed by \textcite{q4-Ball2011}.
They showed that on simply-connected two- and three-dimensional domains for $p ≥ 2$ all weakly differentiable $W^{1,p}$ line fields are orientable \parencite[Thm.~2][]{q4-Ball2011}.
For two-dimensional domains with holes they showed that orientability of a line field is equivalent to orientability on the boundaries of the holes.
For two-dimensional domains with holes they showed that orientability of a line field is equivalent to orientability on the boundaries of the holes \parencite[Prop.~7][]{q4-Ball2011}.
Furthermore they characterise orientability on a hole boundary with the winding number of an auxiliary unit vector valued map.
Intuitively spoken, this auxiliary map turns twice as fast as the line field and if its winding number is even, the line field is orientable.
Intuitively spoken, this auxiliary map turns twice as fast as the line field and if its winding number is even, the line field is orientable.%
\ask{Vielleicht die letzten beiden Sätze weglassen? Das wird technisch so gemacht und es ist auch ein Grund, warum die Technik nicht auf höhere Dimensionen angewendet werden kann. Aber ich finde es nicht so klar verständlich und vielleicht auch nicht so wichtig.}
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