Riemannian submanifolds
BY Chen - Handbook of differential geometry, 2000 - Elsevier
Problems in submanifold theory have been studied since the invention of calculus and it was
started with differential geometry of plane curves. Owing to his studies of how to draw …
started with differential geometry of plane curves. Owing to his studies of how to draw …
[图书][B] Complete embedded minimal surfaces of finite total curvature
D Hoffman, H Karcher - 1997 - Springer
We will survey what is known about minimal surfaces S⊂ R 3, which are complete,
embedded, and have finite total curvature:| K| dA< ∞. The only classically known examples …
embedded, and have finite total curvature:| K| dA< ∞. The only classically known examples …
Properly embedded minimal surfaces with finite total curvature
Among properly embedded minimal surfaces in Euclidean three space, those that have finite
total curvature from a natural and important subclass. The first nontrivial examples, other …
total curvature from a natural and important subclass. The first nontrivial examples, other …
The embedded Calabi–Yau conjecture for finite genus
Suppose that M is a complete, embedded minimal surface in R 3 with an infinite number of
ends, finite genus, and compact boundary. We prove that the simple limit ends of M have …
ends, finite genus, and compact boundary. We prove that the simple limit ends of M have …
Conformal properties in classical minimal surface theory
WH Meeks, J Pérez - Surveys in differential geometry, 2004 - intlpress.com
This is a survey of recent developments in the classical theory of minimal surfaces in R 3
with an emphasis on the conformal properties of these surfaces such as recurrence and …
with an emphasis on the conformal properties of these surfaces such as recurrence and …
The space of properly embedded minimal surfaces with finite total curvature
It is showed that the set of non degenerate properly embedded minimal surfaces with finite
total curvature and fixed topology in ℝ3 has a structure of finite dimensional real-analytic …
total curvature and fixed topology in ℝ3 has a structure of finite dimensional real-analytic …
The Geometry of minimal surfaces of finite genus I: curvature estimates and quasiperiodicity
Let\mathcal M be the space of properly embedded minimal surfaces in ℝ3 with genus zero
and two limit ends, normalized so that every surface M∊\mathcal M has horizontal limit …
and two limit ends, normalized so that every surface M∊\mathcal M has horizontal limit …
Uniqueness of the Riemann minimal examples
We prove that a properly embedded minimal surface in R 3 of genus zero with infinite
symmetry group is a plane, a catenoid, a helicoid or a Riemann minimal example. We …
symmetry group is a plane, a catenoid, a helicoid or a Riemann minimal example. We …
The classification of singly periodic minimal surfaces with genus zero and Scherk-type ends
J Pérez, M Traizet - Transactions of the American Mathematical Society, 2007 - ams.org
Given an integer $ k\geq 2$, let ${\mathcal S}(k) $ be the space of complete embedded
singly periodic minimal surfaces in $\mathbb {R}^ 3$, which in the quotient have genus zero …
singly periodic minimal surfaces in $\mathbb {R}^ 3$, which in the quotient have genus zero …