Expand all Collapse all | Results 1 - 25 of 52 |
1. CMB Online first
Spectral Properties of a Family of Minimal Tori of Revolution in Five-dimensional Sphere The normalized eigenvalues $\Lambda_i(M,g)$ of the Laplace-Beltrami
operator can be considered as functionals on the space of all
Riemannian metrics $g$ on a fixed surface $M$. In recent papers
several explicit examples of extremal metrics were provided.
These metrics are induced by minimal immersions of surfaces in
$\mathbb{S}^3$ or $\mathbb{S}^4$. In the present paper a family
of extremal metrics induced by minimal immersions in $\mathbb{S}^5$
is investigated.
Keywords:extremal metric, minimal surface Category:58J50 |
2. CMB Online first
On the Relation of Real and Complex Lie Supergroups A complex Lie supergroup can be described as a real Lie supergroup
with integrable almost complex structure. The necessary and
sufficient conditions on an almost complex structure on a real
Lie supergroup for defining a complex Lie supergroup are deduced.
The classification of real Lie supergroups with such almost
complex
structures yields a new approach to the known classification
of complex Lie supergroups by complex Harish-Chandra superpairs.
A universal complexification of a real Lie supergroup is
constructed.
Keywords:Lie supergroup, almost complex structure, Harish-Chandra pair, universal complexification Categories:32C11, 58A50 |
3. CMB Online first
The Diffeomorphism Type of Canonical Integrations Of Poisson tensors on Surfaces A surface $\Sigma$ endowed with a Poisson tensor
$\pi$ is known to admit
canonical integration, $\mathcal{G}(\pi)$,
which is a 4-dimensional manifold with a (symplectic) Lie groupoid
structure.
In this short note we show that if $\pi$ is not an area
form on the 2-sphere, then $\mathcal{G}(\pi)$ is diffeomorphic
to the cotangent bundle $T^*\Sigma$. This extends
results by the author and by Bonechi, Ciccoli, Staffolani, and Tarlini.
Keywords:Poisson tensor, Lie groupoid, cotangent bundle Categories:58H05, 55R10, 53D17 |
4. CMB 2014 (vol 58 pp. 69)
Correction to "Infinite Dimensional DeWitt Supergroups and Their Bodies" The Theorem below is a correction to Theorem
3.5 in the article
entitled " Infinite Dimensional DeWitt Supergroups and Their
Bodies" published
in Canad. Math. Bull. Vol. 57 (2) 2014 pp. 283-288. Only part
(iii) of that Theorem
requires correction. The proof of Theorem 3.5 in the original
article failed to separate
the proof of (ii) from the proof of (iii). The proof of (ii)
is complete once it is established
that $ad_a$ is quasi-nilpotent for each $a$ since it immediately
follows that $K$
is quasi-nilpotent. The proof of (iii) is not complete
in the original article. The revision appears as the proof of
(iii) of the revised Theorem below.
Keywords:super groups, body of super groups, Banach Lie groups Categories:58B25, 17B65, 81R10, 57P99 |
5. CMB 2013 (vol 57 pp. 357)
Representation Equivalent Bieberbach Groups and Strongly Isospectral Flat Manifolds Let $\Gamma_1$ and $\Gamma_2$ be Bieberbach groups contained in the
full isometry group $G$ of $\mathbb{R}^n$.
We prove that if the compact flat manifolds $\Gamma_1\backslash\mathbb{R}^n$ and
$\Gamma_2\backslash\mathbb{R}^n$ are strongly isospectral then the Bieberbach groups
$\Gamma_1$ and $\Gamma_2$ are representation equivalent, that is, the
right regular representations $L^2(\Gamma_1\backslash G)$ and
$L^2(\Gamma_2\backslash G)$ are unitarily equivalent.
Keywords:representation equivalent, strongly isospectrality, compact flat manifolds Categories:58J53, 22D10 |
6. CMB 2012 (vol 56 pp. 814)
Quantum Limits of Eisenstein Series and Scattering States We identify the quantum limits of scattering states
for the modular surface. This is obtained through the study of quantum
measures of non-holomorphic Eisenstein series away from the critical
line. We provide a range of stability for the quantum unique
ergodicity theorem of Luo and Sarnak.
Keywords:quantum limits, Eisenstein series, scattering poles Categories:11F72, 58G25, 35P25 |
7. CMB 2011 (vol 56 pp. 127)
Evolution of Eigenvalues along Rescaled Ricci Flow In this paper, we discuss monotonicity formulae of various entropy functionals under various
rescaled versions of Ricci flow. As an application, we prove that the lowest eigenvalue
of a family of geometric operators $-4\Delta + kR$ is monotonic along the
normalized Ricci flow for all $k\ge 1$ provided the initial manifold has
nonpositive total scalar curvature.
Keywords:monotonicity formulas, Ricci flow Categories:58C40, 53C44 |
8. CMB 2011 (vol 56 pp. 366)
Multiple Solutions for Nonlinear Periodic Problems We consider a nonlinear periodic problem driven by a
nonlinear nonhomogeneous differential operator and a
CarathÃ©odory reaction term $f(t,x)$ that exhibits a
$(p-1)$-superlinear growth in $x \in \mathbb{R}$
near $\pm\infty$ and near zero.
A special case of the differential operator is the scalar
$p$-Laplacian. Using a combination of variational methods based on
the critical point theory with Morse theory (critical groups), we
show that the problem has three nontrivial solutions, two of which
have constant sign (one positive, the other negative).
Keywords:$C$-condition, mountain pass theorem, critical groups, strong deformation retract, contractible space, homotopy invariance Categories:34B15, 34B18, 34C25, 58E05 |
9. CMB 2011 (vol 56 pp. 3)
Semiclassical Limits of Eigenfunctions on Flat $n$-Dimensional Tori We provide a proof of a conjecture by Jakobson, Nadirashvili, and
Toth stating
that on an $n$-dimensional flat torus $\mathbb T^{n}$, and the Fourier transform
of squares of the eigenfunctions $|\varphi_\lambda|^2$ of the Laplacian have
uniform $l^n$ bounds that do not depend on the eigenvalue $\lambda$. The proof
is a generalization of an argument by Jakobson, et al. for the
lower dimensional cases. These results imply uniform bounds for semiclassical
limits on $\mathbb T^{n+2}$. We also prove a geometric lemma that bounds the number of
codimension-one simplices satisfying a certain restriction on an
$n$-dimensional sphere $S^n(\lambda)$ of radius $\sqrt{\lambda}$, and we use it in
the proof.
Keywords:semiclassical limits, eigenfunctions of Laplacian on a torus, quantum limits Categories:58G25, 81Q50, 35P20, 42B05 |
10. CMB 2011 (vol 55 pp. 723)
First Variation Formula in Wasserstein Spaces over Compact Alexandrov Spaces We extend results proved by the second author (Amer. J. Math., 2009)
for nonnegatively curved Alexandrov spaces
to general compact Alexandrov spaces $X$ with curvature bounded
below.
The gradient flow of a geodesically convex functional on the quadratic Wasserstein
space $(\mathcal P(X),W_2)$ satisfies the evolution variational inequality.
Moreover, the gradient flow enjoys uniqueness and contractivity.
These results are obtained by proving a first variation formula for
the Wasserstein distance.
Keywords:Alexandrov spaces, Wasserstein spaces, first variation formula, gradient flow Categories:53C23, 28A35, 49Q20, 58A35 |
11. CMB 2011 (vol 54 pp. 396)
Parabolic Geodesics in Sasakian $3$-Manifolds We give explicit parametrizations for all
parabolic geodesics in 3-dimensional Sasakian space forms.
Keywords:parabolic geodesics, pseudo-Hermitian geometry, Sasakian manifolds Category:58E20 |
12. CMB 2011 (vol 54 pp. 693)
Stratified Subcartesian Spaces We show that if the family $\mathcal{O}$ of orbits of all vector fields on
a subcartesian space $P$ is locally finite and each orbit in $\mathcal{O}$
is locally closed, then $\mathcal{O}$ defines a smooth Whitney A
stratification of $P$. We also show that the stratification by orbit type of
the space of orbits $M/G$ of a proper action of a Lie group $G$ on a smooth
manifold $M$ is given by orbits of the family of all vector fields on $M/G$.
Keywords:Subcartesian spaces, orbits of vector fields, stratifications, Whitney Conditions Categories:58A40, 57N80 |
13. CMB 2011 (vol 54 pp. 249)
A Note about Analytic Solvability of Complex Planar Vector Fields with Degeneracies This paper deals with the analytic solvability of a special class of
complex vector fields defined on the real plane, where they are
tangent to
a closed real curve, while off the real curve, they are elliptic.
Keywords:semi-global solvability, analytic solvability, normalization, complex vector fields, condition~($\mathcal P$) Categories:35A01, 58Jxx |
14. CMB 2010 (vol 53 pp. 674)
Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary |
Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary
We study a semilinear elliptic problem on a compact Riemannian
manifold with boundary, subject to an inhomogeneous Neumann
boundary condition. Under various hypotheses on the nonlinear
terms, depending on their behaviour in the origin and infinity, we
prove multiplicity of solutions by using variational arguments.
Keywords:Riemannian manifold with boundary, Neumann problem, sublinearity at infinity, multiple solutions Categories:58J05, 35P30 |
15. CMB 2010 (vol 53 pp. 684)
An Isospectral Deformation on an Infranil-Orbifold
We construct a Laplace isospectral deformation of metrics on an
orbifold quotient of a nilmanifold. Each orbifold in the deformation
contains singular points with order two isotropy. Isospectrality is
obtained by modifying a generalization of Sunada's theorem due to
DeTurck and Gordon.
Keywords:spectral geometry, global Riemannian geometry, orbifold, nilmanifold Categories:58J53, 53C20 |
16. CMB 2010 (vol 53 pp. 542)
Smooth Mappings with Higher Dimensional Critical Sets In this paper we provide lower bounds for the dimension of various critical sets, and we point out some differential maps with high dimensional critical sets.
Categories:58K05, 57R70 |
17. CMB 2009 (vol 53 pp. 122)
A Class of Finsler Metrics with Bounded Cartan Torsion In this paper, we find a class of $(\alpha,\beta)$ metrics which have a bounded Cartan torsion. This class contains all Randers metrics. Furthermore, we give some applications and obtain two corollaries about curvature of this metrics.
Keywords:Finsler manifold, $(\alpha,\beta)$ metric, Cartan torsion, R-quadratic, flag curvature Category:58E20 |
18. CMB 2009 (vol 53 pp. 340)
Regular Points of a Subcartesian Space We discuss properties of the regular part $S_{\operatorname{reg}}$ of
a subcartesian space $S$. We show that $S_{\operatorname{reg}}$ is open and dense in
$S$ and the restriction to $ S_{\operatorname{reg}}$ of the tangent
bundle space of $S$ is locally trivial.
Keywords:differential structures, singular and regular points Category:58A40 |
19. CMB 2009 (vol 52 pp. 18)
Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds In this paper we study holomorphic maps between almost Hermitian
manifolds. We obtain a new criterion for the harmonicity of such
holomorphic maps, and we deduce some applications to horizontally
conformal holomorphic submersions.
Keywords:almost Hermitian manifolds, harmonic maps, harmonic morphism Categories:53C15, 58E20 |
20. CMB 2009 (vol 52 pp. 66)
Huber's Theorem for Hyperbolic Orbisurfaces We show that for compact orientable hyperbolic orbisurfaces, the
Laplace spectrum determines the length spectrum as well as the
number of singular points of a given order. The converse also holds, giving
a full generalization of Huber's theorem to the setting of
compact orientable hyperbolic orbisurfaces.
Keywords:Huber's theorem, length spectrum, isospectral, orbisurfaces Categories:58J53, 11F72 |
21. CMB 2008 (vol 51 pp. 467)
Coupled Vortex Equations on Complete KÃ¤hler Manifolds In this paper, we first investigate the Dirichlet
problem for coupled vortex equations. Secondly, we give existence
results for solutions of the coupled vortex equations on a class
of complete noncompact K\"ahler manifolds which include
simply-connected strictly negative curved manifolds, Hermitian
symmetric spaces of noncompact type and strictly pseudo-convex
domains equipped with the Bergmann metric.
Categories:58J05, 53C07 |
22. CMB 2008 (vol 51 pp. 249)
On the Inner Radius of a Nodal Domain Let $M$ be a closed Riemannian manifold.
We consider the inner radius of a nodal domain for a large eigenvalue $\lambda$.
We give upper and lower bounds on the inner radius of the type
$C/\lambda^\alpha(\log\lambda)^\beta$. Our proof is based on
a local behavior of eigenfunctions discovered by Donnelly and
Fefferman and a Poincar\'{e} type inequality proved by Maz'ya.
Sharp lower bounds are known
only in dimension two. We give an account of this case too.
Categories:58J50, 35P15, 35P20 |
23. CMB 2008 (vol 51 pp. 100)
Dynamical Zeta Function for Several Strictly Convex Obstacles The behavior of the dynamical zeta function $Z_D(s)$ related to
several strictly convex disjoint obstacles is similar to that of the
inverse $Q(s) = \frac{1}{\zeta(s)}$ of the Riemann zeta function
$\zeta(s)$. Let $\Pi(s)$ be the series obtained from $Z_D(s)$ summing
only over primitive periodic rays. In this paper we examine the
analytic singularities of $Z_D(s)$ and $\Pi(s)$ close to the line $\Re
s = s_2$, where $s_2$ is the abscissa of absolute convergence of the
series obtained by the second iterations of the primitive periodic
rays. We show that at least one of the functions $Z_D(s), \Pi(s)$
has a singularity at $s = s_2$.
Keywords:dynamical zeta function, periodic rays Categories:11M36, 58J50 |
24. CMB 2007 (vol 50 pp. 447)
Generalizations of Frobenius' Theorem on Manifolds and Subcartesian Spaces Let $\mathcal{F}$ be a family of vector fields on a manifold or a
subcartesian space spanning a distribution $D$. We prove that an orbit $O$
of $\mathcal{F}$ is an integral manifold of $D$ if $D$ is involutive on $O$
and it has constant rank on $O$. This result implies Frobenius' theorem, and
its various generalizations, on manifolds as well as on subcartesian spaces.
Keywords:differential spaces, generalized distributions, orbits, Frobenius' theorem, Sussmann's theorem Categories:58A30, 58A40 |
25. CMB 2007 (vol 50 pp. 113)
Hermitian Harmonic Maps into Convex Balls In this paper, we consider Hermitian harmonic maps from
Hermitian manifolds into convex balls. We prove that there exist
no non-trivial Hermitian harmonic maps from closed Hermitian
manifolds into convex balls, and we use the heat flow method to
solve the Dirichlet problem for Hermitian harmonic maps when the
domain is a compact Hermitian manifold with non-empty boundary.
Keywords:Hermitian harmonic map, Hermitian manifold, convex ball Categories:58E15, 53C07 |