16:15 Uhr | Filip Rindler (Cambridge) | Directional oscillations, concentrations, and compensated
compactness via microlocal compactness forms
Microlocal compactness forms (MCFs) are a new tool to study oscillations
and concentrations in $L^p$-bounded sequences of functions. Decisively,
MCFs retain information about the location, value distribution, and
direction of oscillations and concentrations, thus extending both the
theory of (generalized) Young measures and the theory of $H$-measures.
Since in $L^p$-spaces oscillations and concentrations precisely
discriminate between weak and strong compactness, MCFs allow to quantify
the difference between these two notions of compactness. The definition
involves a Fourier variable, whereby also differential constraints on
the functions in the sequence can be investigated easily. Furthermore,
pointwise restrictions are reflected in the MCF as well, paving the way
for applications to Tartar's framework of compensated compactness;
consequently, we establish a new weak-to-strong compactness theorem in a
"geometric" way. Moreover, the hierarchy of oscillations with regard to
slow and fast scales can be investigated as well since this information
is also is reflected in the generated MCF.
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17:45 Uhr | Barbara Nelli (Universitá di L'Aquila) | Minimal surfaces with two ends in $\mathbb H^2 \times \mathbb R$
How the shape of the ends of a minimal surface determines the
surface itself?
We discuss the problem for minimal surfaces with two ends in $\mathbb H^2\times \mathbb R$.
Namely, we prove a Schoen type theorem for such surfaces.
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