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The matching problem between functional shapes via a BV-penalty term: a -convergence result
In this paper we study a variant of the matching model between functional
shapes introduced in \cite{ABN}. Such a model allows to compare surfaces
equipped with a signal and the matching energy is defined by the -norm of
the signal on the surface and a varifold-type attachment term.
In this work we study the problem with fixed geometry which means that we
optimize the initial signal (supported on the initial surface) with respect to
a target signal supported on a different surface. In particular, we consider a
or -penalty for the signal instead of its -norm. Several
numerical examples are shown in order to prove that the -penalty improves
the quality of the matching. Moreover, we prove a -convergence result
for the discrete matching energy towards the continuous-one
Toric systems and mirror symmetry
Hille and Perling associate to every cyclic full strongly exceptional
sequence of line bundles on a toric weak Fano surface a toric system, which
defines a new toric surface. In this note we interprete this construction as an
instance of mirror symmetry and extend it to a duality on the set toric weak
Fano surfaces equiped with a cyclic full strongly exceptional sequence
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