76. CJM 2001 (vol 53 pp. 780)
 Nicolaescu, Liviu I.

SeibergWitten Invariants of Lens Spaces
We show that the SeibergWitten invariants of a lens space determine
and are determined by its CassonWalker invariant and its
ReidemeisterTuraev torsion.
Keywords:lens spaces, Seifert manifolds, SeibergWitten invariants, CassonWalker invariant, Reidemeister torsion, eta invariants, DedekindRademacher sums Categories:58D27, 57Q10, 57R15, 57R19, 53C20, 53C25 

77. CJM 2000 (vol 52 pp. 757)
 Hanani, Abdellah

Le problÃ¨me de Neumann pour certaines Ã©quations du type de MongeAmpÃ¨re sur une variÃ©tÃ© riemannienne
Let $(M_n,g)$ be a strictly convex riemannian manifold with
$C^{\infty}$ boundary. We prove the existence\break
of classical solution for the nonlinear elliptic partial
differential equation of MongeAmp\`ere:\break
$\det (u\delta^i_j + \nabla^i_ju) = F(x,\nabla u;u)$ in $M$ with a
Neumann condition on the boundary of the form $\frac{\partial
u}{\partial \nu} = \varphi (x,u)$, where $F \in C^{\infty} (TM
\times \bbR)$ is an everywhere strictly positive function
satisfying some assumptions, $\nu$ stands for the unit normal
vector field and $\varphi \in C^{\infty} (\partial M \times \bbR)$
is a nondecreasing function in $u$.
Keywords:connexion de LeviCivita, Ã©quations de MongeAmpÃ¨re, problÃ¨me de Neumann, estimÃ©es a priori, mÃ©thode de continuitÃ© Categories:35J60, 53C55, 58G30 

78. CJM 1999 (vol 51 pp. 1123)
 Arnold, V. I.

First Steps of Local Contact Algebra
We consider germs of mappings of a line to contact space and
classify the first simple singularities up to the action of
contactomorphisms in the target space and diffeomorphisms of the
line. Even in these first cases there arises a new interesting
interaction of local commutative algebra with contact structure.
Keywords:contact manifolds, local contact algebra, Diracian, contactian Categories:53D10, 14B05 

79. CJM 1999 (vol 51 pp. 449)
 Bahn, Hyoungsick; Ehrlich, Paul

A BrunnMinkowski Type Theorem on the Minkowski Spacetime
In this article, we derive a BrunnMinkowski type theorem
for sets bearing some relation to the causal structure
on the Minkowski spacetime $\mathbb{L}^{n+1}$. We also
present an isoperimetric inequality in the Minkowski
spacetime $\mathbb{L}^{n+1}$ as a consequence of this
BrunnMinkowski type theorem.
Keywords:Minkowski spacetime, BrunnMinkowski inequality, isoperimetric inequality Categories:53B30, 52A40, 52A38 

80. CJM 1998 (vol 50 pp. 1298)
 Milson, Robert

Imprimitively generated Liealgebraic Hamiltonians and separation of variables
Turbiner's conjecture posits that a Liealgebraic Hamiltonian
operator whose domain is a subset of the Euclidean plane admits a
separation of variables. A proof of this conjecture is given in
those cases where the generating Liealgebra acts imprimitively.
The general form of the conjecture is false. A counterexample is
given based on the trigonometric OlshanetskyPerelomov potential
corresponding to the $A_2$ root system.
Categories:35Q40, 53C30, 81R05 

81. CJM 1997 (vol 49 pp. 1162)
 Ku, HsuTung; Ku, MeiChin; Zhang, XinMin

Isoperimetric inequalities on surfaces of constant curvature
In this paper we introduce the concepts of hyperbolic and elliptic
areas and prove uncountably many new geometric isoperimetric
inequalities on the surfaces of constant curvature.
Keywords:Gaussian curvature, GaussBonnet theorem, polygon, pseudopolygon, pseudoperimeter, hyperbolic surface, Heron's formula, analytic and geometric isoperimetric inequalities Categories:51M10, 51M25, 52A40, 53C20 

82. CJM 1997 (vol 49 pp. 1323)
 Sankaran, Parameswaran; Zvengrowski, Peter

Stable parallelizability of partially oriented flag manifolds II
In the first paper with the same title the authors
were able to determine all partially oriented flag
manifolds that are stably parallelizable or
parallelizable, apart from four infinite families
that were undecided. Here, using more delicate
techniques (mainly Ktheory), we settle these
previously undecided families and show that none of
the manifolds in them is stably parallelizable,
apart from one 30dimensional manifold which still
remains undecided.
Categories:57R25, 55N15, 53C30 

83. CJM 1997 (vol 49 pp. 696)
84. CJM 1997 (vol 49 pp. 417)
 Boe, Brian D.; Fu, Joseph H. G.

Characteristic cycles in Hermitian symmetric spaces
We give explicit combinatorial expresssions for the characteristic
cycles associated to certain canonical sheaves on Schubert varieties
$X$ in the classical Hermitian symmetric spaces: namely the
intersection homology sheaves $IH_X$ and the constant sheaves $\Bbb
C_X$. The three main cases of interest are the Hermitian symmetric
spaces for groups of type $A_n$ (the standard Grassmannian), $C_n$
(the Lagrangian Grassmannian) and $D_n$. In particular we find that
$CC(IH_X)$ is irreducible for all Schubert varieties $X$ if and only
if the associated Dynkin diagram is simply laced. The result for
Schubert varieties in the standard Grassmannian had been established
earlier by Bressler, Finkelberg and Lunts, while the computations in
the $C_n$ and $D_n$ cases are new.
Our approach is to compute $CC(\Bbb C_X)$ by a direct geometric
method, then to use the combinatorics of the KazhdanLusztig
polynomials (simplified for Hermitian symmetric spaces) to compute
$CC(IH_X)$. The geometric method is based on the fundamental formula
$$CC(\Bbb C_X) = \lim_{r\downarrow 0} CC(\Bbb C_{X_r}),$$ where the
$X_r \downarrow X$ constitute a family of tubes around the variety
$X$. This formula leads at once to an expression for the coefficients
of $CC(\Bbb C_X)$ as the degrees of certain singular maps between
spheres.
Categories:14M15, 22E47, 53C65 

85. CJM 1997 (vol 49 pp. 359)
 Sawyer, P.

Estimates for the heat kernel on $\SL (n,{\bf R})/\SO (n)$
In \cite{Anker}, JeanPhilippe Anker conjectures an upper bound for the
heat kernel of a symmetric space of noncompact type. We show in this
paper that his prediction is verified for the space of positive
definite $n\times n$ real matrices.
Categories:58G30, 53C35, 58G11 
