
SIGMA 3 (2007), 081, 7 pages arXiv:0708.2170
http://dx.doi.org/10.3842/SIGMA.2007.081
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson
Future Directions of Research in Geometry: A Summary of the Panel Discussion at the 2007 Midwest Geometry Conference
Edited by Lawrence J. Peterson
University of North Dakota, Grand Forks, North Dakota, USA
Received August 09, 2007; Published online August 15, 2007
Abstract
The 2007 Midwest Geometry Conference included a panel discussion
devoted to open problems and the general direction of future research
in fields related to the main themes of the conference. This paper
summarizes the comments made during the panel discussion.
Key words:
determinants; differential complexes; differential geometry; Einstein metrics; GJMS operators; global invariants; heat kernel; Kähler metrics; Qcurvature; Sobolev inequalities.
pdf (166 kb)
ps (131 kb)
tex (12 kb)
References
 Chen B.Y., Wei S.W., Geometry of submanifolds of warped
product Riemannian manifolds I×_{f} S^{m1}(k) and applications
to pharmonic and quasiregular mappings, submitted.
 Chen X., LeBrun C., Weber B., On conformally Kähler,
Einstein manifolds, arXiv:0705.0710.
 Colesanti A., Salani P., The BrunnMinkowski inequality for
pcapacity of convex bodies, Math. Ann. 327 (2003), 459479.
 Derdzinski A., Selfdual Kähler manifolds and
Einstein manifolds of dimension four, Comp.
Math. 49 (1983), 405433.
 Deser S., Conformal anomalies revisited: closed form
effective actions in D ³ 4, Nuclear Phys. B Proc. Suppl.
88 (2000), 204209.
 Graham C.R., Jenne R., Mason L.J., Sparling G.A.J.,
Conformally invariant powers of the Laplacian, I: existence,
J. London Math. Soc. (2) 46 (1992), 557565.
 Guillarmou C., Generalized Krein formula and
determinants for even dimensional PoincaréEinstein manifolds,
math.SP/0512173.
 Patterson S.J., Perry P.A., The divisor of Selberg's
zeta function for Kleinian groups, Appendix A by Charles
Epstein, Duke Math. J. 106 (2001), 321390.
 Seshadri N., Some notes on analytic torsion of the Rumin
complex on contact manifolds, arXiv:0704.1982.
 Troyanov M., Parabolicity of manifolds, Siberian Adv. Math. 9 (1999), 125150.
 Vogan D.A. Jr., Wallach N.R., Intertwining
operators for real reductive groups, Adv. Math.
82 (1990), 203243.

