48,069 research outputs found
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic
in Lorentzian conformal geometry which parallels the theory of Willmore
surfaces in , are studied in this paper. We define two kinds of transforms
for such a surface, which produce the so-called left/right polar surfaces and
the adjoint surfaces. These new surfaces are again conformal Willmore surfaces.
For them holds interesting duality theorem. As an application spacelike
Willmore 2-spheres are classified. Finally we construct a family of homogeneous
spacelike Willmore tori.Comment: 19 page
Complete stationary surfaces in with total curvature
Applying the general theory about complete spacelike stationary (i.e. zero
mean curvature) surfaces in 4-dimensional Lorentz space , we
classify those regular algebraic ones with total Gaussian curvature . Such surfaces must be oriented and be congruent to either
the generalized catenoids or the generalized enneper surfaces. For
non-orientable stationary surfaces, we consider the Weierstrass representation
on the oriented double covering (of genus ) and generalize
Meeks and Oliveira's M\"obius bands. The total Gaussian curvature are shown to
be at least when is
algebraic-type. We conjecture that there do not exist non-algebraic examples
with .Comment: 22 page
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic
in Lorentzian conformal geometry which parallels the theory of Willmore
surfaces in , are studied in this paper. We define two kinds of transforms
for such a surface, which produce the so-called left/right polar surfaces and
the adjoint surfaces. These new surfaces are again conformal Willmore surfaces.
For them holds interesting duality theorem. As an application spacelike
Willmore 2-spheres are classified. Finally we construct a family of homogeneous
spacelike Willmore tori.Comment: 19 page
Applications of shuffle product to restricted decomposition formulas for multiple zeta values
In this paper we obtain a recursive formula for the shuffle product and apply
it to derive two restricted decomposition formulas for multiple zeta values
(MZVs). The first formula generalizes the decomposition formula of Euler and is
similar to the restricted formula of Eie and Wei for MZVs with one strings of
1's. The second formula generalizes the previous results to the product of two
MZVs with one and two strings of 1's respectively.Comment: 11 page
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