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New examples of zero mean curvature surfaces in the threedimensional anti deSitter space
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New examples of zero mean curvature surfaces in the threedimensional anti deSitter space
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Description
Identifier
Thesis
2233
Author
LeMay, Steven Robert, 1983
Title
New
examples
of
zero
mean
curvature
surfaces
in the
threedimensional
anti
deSitter
space
Publisher
Central Connecticut State University
Date of Publication
2012
Resource Type
Master's Thesis
Abstract
This
work
deals
with the
construction
of
zero
mean
curvature
surfaces
in the
three
dimensional
anti
deSitter
space
. The
method
that was
used
was to
look
for
examples
that
can
be
described
using
polynomial
equations
.
More
precisely
,
we
are
looking
for "
algebraic
"
examples
of
zero
mean
curvature
surfaces
.
Success
was
found
in
finding
new
examples
.
Actually
the
author
proved
that if
we
used
some
polynomial
equations
previously
discovered
by
Blaine
Lawson
to
study
a
similar
problem
in the
three
dimensional
sphere
, these
equations
will also
produce
examples
with
zero
mean
curvature
in the
three
dimensional
anti
deSitter
space
. This
is
considered
the
main
result
of the
thesis
. The
family
of
examples
that were
found
is
so
rich
that
it
shows
the
existence
of
algebraic
examples
of any
order
; that
is
,
examples
produced
with
equations
involving
a
polynomial
of any
desire
degree
. This
thesis
is
written
to be as
selfcontained
as
possible
. In
regard
with the
method
used
to
prove
the
main
result
,
two
different
approaches
are
explained
to
prove
that a
particular
surface
has
zero
mean
curvature
.
One
of them
uses
a
parametrization
of the
surface
and the
other
uses
the
polynomial
that
describes
the
surface
.
Even
though
both
methods
were
thoroughly
studied
in the
thesis
, the
former
one
was
used
to
prove
the
main
result
Subject
Curvature  Mathematical models
Surfaces of constant curvature
Mathematics
Mathematical analysis
Department
Department of Mathematical Sciences
Advisor
Perdomo, Oscar
Type
Text
Digital Format
application/pdf
Language
eng
OCLC number
824457096
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