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About the uniqueness of conformal metrics with pre scribed scalar and mean curvatures on compact manifolds with boundary.
(2011-10-14)
Let (Mⁿ, g) be an n – dimensional compact Riemannian manifold with boundary with n ≥ 2.
In this paper we study the uniquensess of metrics in the conformal class of the metric g having the same scalar curvature in M, aM, ...
A priori estimates of the prescribed scalar curvature on the sphere.
(2018-07-18)
This paper considers the prescribed scalar curvature problem on the sphere for n ≥ 3.
Given a prescribed scalar curvature function K : Sn → R and a centered dilation defined
by Fy = Σ−1 ◦ Dβ ◦ Σ, y ∈ Bn+1, where Σ is the ...
Finite topology self-translating surfaces for the mean curvature flow in R3
(Elsevier, 2017)
Finite topology self-translating surfaces for the mean curva-ture flow constitute a key element in the analysis of TypeII singularities from a compact surface because they arise as lim-its after suitable blow-up scalings ...
Lower Bound for the First Steklov Eigenvalue.
(2018-07-18)
In this paper we find lower bounds for the first Steklov eigenvalue in Riemannian
n-manifolds, n = 2, 3, with non-positive sectional curvature.
Large Conformal metrics with prescribed sign-changing Gauss curvature
(Springer, 2015)
Let (M, g) be a two dimensional compact Riemannian manifold of genus g(M) > . Let f be a smooth function on M such that
f >= 0, f not equivalent to 0, min(M) f = 0.
Let be any set of points at which f (P-i) = 0 and ...
Stable minimal cones in ℝ8 and ℝ9 with constant scalar curvature
(Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas, 2002)
In this paper we prove that if M ⊏ ℝn , n = 8 or n = 9, is a n - 1 dimensional stable minimal complete cone such that its scalar curvature varies radially, then M must be either a hyperplane or a Clifford minimal cone. ...
Cosmic in ation in a landscape of heavy-
(IOP Publishing and Sissa Medialab, 2013)
Heavy isocurvature elds may have a strong in
uence on the low energy dynamics
of curvature perturbations during in
ation, as long as the in
ationary trajectory becomes
non-geodesic in the multi- eld target space (the ...
Uniqueness of conformal metrics with prescribed scalar and mean curvatures on compact manifolds with boundary
(Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas, 2010)
Departamento de Matemáticas, Universidad del Valle, Calle 13 No. 100 - 00, Cali, ColombiaLet $(M^n, g)$ be a compact manifold with boundary and $n \geq 2$. In this paper we prove the variational characterization of the ...
Interface dynamics in semilinear wave equations
(Springer, 2020)
We consider the wave equation epsilon(2)(-partial derivative(2)(t) + Delta)u + f(u) = 0 for 0 < epsilon << 1, where f is the derivative of a balanced, double-well potential, the model case being f(u) = u - u(3). For equations ...
Total absolute curvature of curves in lorentz manifolds
(Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas, 1993)
The total absolute curvature of manifolds has been discussed several times and some papers about it already belong to the classical literature on that topics. All of them deal with manifolds inmersed in Riemannian spaces.