90 research outputs found
A threshold phenomenon for embeddings of into Orlicz spaces
We consider a sequence of positive smooth critical points of the
Adams-Moser-Trudinger embedding of into Orlicz spaces. We study its
concentration-compactness behavior and show that if the sequence is not
precompact, then the liminf of the -norms of the functions is greater
than or equal to a positive geometric constant.Comment: 14 Page
The substrate lends a hand
Duramycin is a small post-translationally modified peptide with antibody-like affinity for phosphatidylethanolamine. As it turns out, the same functionality that is essential for duramycin activity helps to catalyze the formation of its conformationally constrained and compact polycyclic architecture
A classification theorem for Helfrich surfaces
In this paper we study the functional \SW_{\lambda_1,\lambda_2}, which is
the the sum of the Willmore energy, -weighted surface area, and
-weighted volume, for surfaces immersed in . This coincides
with the Helfrich functional with zero `spontaneous curvature'. Our main result
is a complete classification of all smooth immersed critical points of the
functional with and small norm of tracefree curvature. In
particular we prove the non-existence of critical points of the functional for
which the surface area and enclosed volume are positively weighted.Comment: 21 page
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