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Finite topology self-translating surfaces for the mean curvature flow in R-3
(2017)
Finite topology self-translating surfaces for the mean curvature flow constitute a key element in the analysis of Type II singularities from a compact surface because they arise as limits after suitable blow-up scalings ...
Nonlocal Delaunay surfaces
(2016)
We construct codimension 1 surfaces of any dimension that minimize a periodic nonlocal perimeter functional among surfaces that are periodic, cylindrically symmetric and decreasing. These surfaces may be seen as a nonlocal ...
The Craighero-Gattazzo surface is simply connected
(2017)
We show that the Craighero-Gattazzo surface, the minimal resolution of an explicit complex quintic surface with four elliptic singularities, is simply connected. This was conjectured by Dolgachev and Werner, who proved ...
On Z/3-Godeaux Surfaces
(2018)
We prove that Godeaux-Reid surfaces with torsion group Z/3 have topological fundamental group Z/3. For this purpose, we describe degenerations to stable KSBA surfaces with one 1/4 (1, 1) singularity, whose minimal resolution ...
Nonlocal s-minimal surfaces and Lawson cones
(2018)
The nonlocal s-fractional minimal surface equation for Sigma = partial derivative E where E is an open set in R-N is given by H-Sigma(s)(p) := integral(RN) chi E(x) - chi E-c(x)/vertical bar x - p vertical bar N + s dx = ...