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44
The CalabiYau conjectures for embedded surfaces
, 2004
"... In this paper we will prove the CalabiYau conjectures for embedded surfaces (i.e., surfaces without selfintersection). In fact, we will prove considerably more. The heart of our argument is very general and should apply to a variety of situations, as will be more apparent once we describe the main ..."
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Cited by 20 (2 self)
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In this paper we will prove the CalabiYau conjectures for embedded surfaces (i.e., surfaces without selfintersection). In fact, we will prove considerably more. The heart of our argument is very general and should apply to a variety of situations, as will be more apparent once we describe the main steps of the proof later in the introduction.
The Geometry of Periodic Minimal Surfaces
, 1993
"... this paper we shall demonstrate a surprising relationship between the topology of a properly embedded periodic minimal surface in R ..."
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Cited by 20 (0 self)
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this paper we shall demonstrate a surprising relationship between the topology of a properly embedded periodic minimal surface in R
Maximal surfaces with singularities in Minkowski space
 Hokkaido Math. J
"... Abstract. We shall investigate maximal surfaces in Minkowski 3space with singularities. Although the plane is the only complete maximal surface without singular points, there are many other complete maximal surfaces with singularities and we show that they satisfy an Ossermantype inequality. ..."
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Cited by 14 (4 self)
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Abstract. We shall investigate maximal surfaces in Minkowski 3space with singularities. Although the plane is the only complete maximal surface without singular points, there are many other complete maximal surfaces with singularities and we show that they satisfy an Ossermantype inequality.
Spacelike CMC 1 surfaces with elliptic ends
"... Dedicated to Professor Takeshi Sasaki on the occasion of his sixtieth birthday Abstract. We show that an Ossermantype inequality holds for spacelike surfaces of constant mean curvature 1 with singularities and with elliptic ends in de Sitter 3space. An immersed end of a constant mean curvature 1 s ..."
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Cited by 12 (5 self)
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Dedicated to Professor Takeshi Sasaki on the occasion of his sixtieth birthday Abstract. We show that an Ossermantype inequality holds for spacelike surfaces of constant mean curvature 1 with singularities and with elliptic ends in de Sitter 3space. An immersed end of a constant mean curvature 1 surface is an “elliptic end ” if the monodromy representation at the end is diagonalizable with eigenvalues in the unit circle. We also give a necessary and sufficient condition for equality in the inequality to hold, and in the process of doing this we derive a condition for determining when elliptic ends are embedded.
On equilibrium points of logarithmic and Newtonian potentials
 J. London Math. Soc
, 1993
"... Let j{z) = Yu? \ a}l ( z ~ z))> where z, ^ 0 and ^"J^l/k^l < oo. Then /can be realized as the complex conjugate of the gradient of a logarithmic potential or, for integral a}, as the logarithmic derivative of a meromorphic function. We investigate conditions on a} and zj that guarantee that / has ..."
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Cited by 12 (5 self)
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Let j{z) = Yu? \ a}l ( z ~ z))> where z, ^ 0 and ^"J^l/k^l < oo. Then /can be realized as the complex conjugate of the gradient of a logarithmic potential or, for integral a}, as the logarithmic derivative of a meromorphic function. We investigate conditions on a} and zj that guarantee that / has zeros. In the potential theoretic setting, this asks whether certain logarithmic potentials with discrete mass distribution have equilibrium points. 1.
COMPLETE MINIMAL SURFACES IN R³
, 1999
"... In this paper we review some topics on the theory of complete minimal surfaces in three dimensional Euclidean space. ..."
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Cited by 11 (1 self)
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In this paper we review some topics on the theory of complete minimal surfaces in three dimensional Euclidean space.
Conformal invariants and partial differential equations
 Math.Soc.(N.S.)42 (2005), 365–393 (electronic), http://dx.doi.org/10.1090/S027309790501058X. MR 2149088 (2006b:53045
"... 1 A blow up sequence of functions; when n ≥ 3 3 ..."
GENUSONE HELICOIDS FROM A VARIATIONAL POINT OF VIEW
, 2007
"... In this paper, we prove by variational means the existence of a complete, properly embedded, genusone minimal surface in R 3 that is asymptotic to a helicoid at infinity. We also prove existence of surfaces that are asymptotic to a helicoid away from the helicoid’s axis, but that have infinitely ma ..."
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Cited by 8 (2 self)
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In this paper, we prove by variational means the existence of a complete, properly embedded, genusone minimal surface in R 3 that is asymptotic to a helicoid at infinity. We also prove existence of surfaces that are asymptotic to a helicoid away from the helicoid’s axis, but that have infinitely many handles arranged periodically