The positive mass theorem for ALE manifolds

Mattias Dahl

Banach Center Publications (1997)

  • Volume: 41, Issue: 1, page 133-142
  • ISSN: 0137-6934

Abstract

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We show what extra condition is necessary to be able to use the positive mass argument of Witten [12] on an asymptotically locally euclidean manifold. Specifically we show that the 'generalized positive action conjecture' holds if one assumes that the signature of the manifold has the correct value.

How to cite

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Dahl, Mattias. "The positive mass theorem for ALE manifolds." Banach Center Publications 41.1 (1997): 133-142. <http://eudml.org/doc/252208>.

@article{Dahl1997,
abstract = {We show what extra condition is necessary to be able to use the positive mass argument of Witten [12] on an asymptotically locally euclidean manifold. Specifically we show that the 'generalized positive action conjecture' holds if one assumes that the signature of the manifold has the correct value.},
author = {Dahl, Mattias},
journal = {Banach Center Publications},
keywords = {asymptotically locally Euclidean manifold; spin geometry; positive mass theorem},
language = {eng},
number = {1},
pages = {133-142},
title = {The positive mass theorem for ALE manifolds},
url = {http://eudml.org/doc/252208},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Dahl, Mattias
TI - The positive mass theorem for ALE manifolds
JO - Banach Center Publications
PY - 1997
VL - 41
IS - 1
SP - 133
EP - 142
AB - We show what extra condition is necessary to be able to use the positive mass argument of Witten [12] on an asymptotically locally euclidean manifold. Specifically we show that the 'generalized positive action conjecture' holds if one assumes that the signature of the manifold has the correct value.
LA - eng
KW - asymptotically locally Euclidean manifold; spin geometry; positive mass theorem
UR - http://eudml.org/doc/252208
ER -

References

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  1. [1] L. Andersson and M. Dahl, ALE manifolds with nonnegative scalar curvature, in preparation. Zbl0946.53021
  2. [2] S. Bando, A. Kasue and H. Nakajima, On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth, Inv. Math. 97 (1989), 313-349. Zbl0682.53045
  3. [3] R. Bartnik, The mass of an asymptotically flat manifold, Comm. on Pure and Appl. Math. 39 (1986), 661-693. Zbl0598.53045
  4. [4] P. B. Gilkey, The geometry of spherical space form groups, Series in Pure Mathematics, vol. 7, World Scientific, Singapore, 1989. Zbl0789.57001
  5. [5] R.E. Greene, P. Petersen and Shunhui Zhu, Riemannian manifolds of faster than quadratic curvature decay, Internat. Math. Res. Notices. 9 (1994). Zbl0833.53037
  6. [6] P. B. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Diff. Geom. 29 (1989), 665-683. Zbl0671.53045
  7. [7] P. B. Kronheimer, A Torelli-type theorem for gravitational instantons, J. Diff. Geom. 29 (1989), 685-697. Zbl0671.53046
  8. [8] H. B. Lawson and M.-L. Michelson, Spin geometry, Princeton University Press, Princeton, 1989. 
  9. [9] C. LeBrun, Counterexamples to the generalized positive action conjecture, C.M.P. 118 (1988), 591-596. Zbl0659.53050
  10. [10] M.Y. Wang, Parallel spinors and parallel forms, Ann. Global Anal. Geom. 7 (1989), 59-68. Zbl0688.53007
  11. [11] M.Y. Wang, On non-simply connected manifolds with non-trivial parallel spinors, Ann. Global Anal. Geom. 13 (1995), 31-42. Zbl0826.53041
  12. [12] E. Witten, A new proof of the positive energy theorem, Comm. Math. Phys. 80 (1981), 381-402. Zbl1051.83532
  13. [13] J.A. Wolf, Spaces of constant curvature, McGraw-Hill, 1967. Zbl0162.53304

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