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On the contact equivalence problem of second order ODEs which are quadratic with respect to the second order derivative
On the contact equivalence problem of second order ODEs quadratic second order derivative Differential Geometry
2012/6/19
In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form $y"{}^2+A(x,y,y') y"+B(x,y,y')=0$ to be equivalent under the action of the...
Remarks on the extension of the Ricci flow
Remarks the extension of the Ricci flow Differential Geometry
2012/6/19
We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.
Nullspaces of Conformally Invariant Operators. Applications to $Q_{k}$-curvature
Spectral geometry conformal geometry nodal sets Qk-curvature
2012/6/19
We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfu...
The aim of this note is to extend the notion of commutativity of vector fields to the category of singular foliations, using Nambu structures, i.e. integrable multi-vector fields. We will show some ba...
Frobenius 3-folds via singular flat 3-webs
Frobenius 3-folds singular flat 3-webs Differential Geometry
2012/6/15
We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ sa...
Optimal Riemannian metric for a volumorphism and a mean ergodic theorem in complete global Alexandrov nonpositively curved spaces
Optimal Riemannian metric volumorphism mean ergodic theorem complete global Alexandrov nonpositively curved spaces Differential Geometry
2012/6/15
In this paper we give a natural condition for when a volumorphism on a Riemannian manifold $(M,g)$ is actually an isometry with respect to some other, optimal, Riemannian metric $h$. We consider the n...
Nonpositively curved manifolds containing a prescribed nonpositively curved hypersurface
Nonpositively curved manifolds prescribed nonpositively curved hypersurface Differential Geometry
2012/6/9
We use pinched smooth hyperbolization to show that every closed, nonpositively curved $n$-dimensional manifold $M$ can be embedded as a totally geodesic submanifold of a closed, nonpositively curved $...
Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation
Existence and Blow-Up Behavior Solutions of the Generalized Jang Equation Differential Geometry
2012/6/9
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study o...
Maximization of the second conformal eigenvalue of spheres
Maximization the second conformal eigenvalue spheres Spectral Theory
2012/6/14
We establish in this paper an upper bound on the second eigenvalue of n-dimensional spheres in the conformal class of the round sphere. This upper bound holds in all dimensions and is asymptotically s...
Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps
Analytic torsion Reidemeister torsion hyperbolic 3-manifolds cusps Spectral Theory
2012/6/14
For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of ...
Quasi-umbilical affine hypersurfaces congruent to their centre map
affine differential geometry quasi-umbilical center map Differential Geometry
2012/6/12
In this paper, we study strictly convex affine hypersurfaces centroaffinely congruent to their centre map, in the case when the shape operator has two distinct eigenvalues: one of multiplicity 1, and ...
Collapsing and essential coverings
the Gromov-Hausdorff convergence Alexandrov spaces Betti numbers
2012/5/25
In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essenti...
New logarithmic Sobolev inequalities and an ε-regularity theorem for the Ricci flow
New logarithmic Sobolev inequalities ε-regularity theorem Ricci flow Differential Geometry
2012/5/24
In this note we prove a new \epsilon-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) in the final t...
Witten's perturbation on strata
Morse inequalities ideal boundary condition Thom-Mather stratification Witten’s perturbation
2012/5/24
The main result is a version of Morse inequalities for the minimum and maximum ideal boundary conditions of the de Rham complex on strata of compact Thom-Mather stratifications, endowed with adapted m...
No breathers theorem for some noncompact Ricci flows
No breathers theorem noncompact Ricci flows Differential Geometry
2012/5/24
Under suitable conditions near infinity and assuming boundedness of curvature tensor, we prove a no breathers theorem in the spirit of Ivey-Perelman for some noncompact Ricci flows. These include Ricc...