# The positive mass theorem for ALE manifolds

Banach Center Publications (1997)

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

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topDahl, 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

top- [1] L. Andersson and M. Dahl, ALE manifolds with nonnegative scalar curvature, in preparation. Zbl0946.53021
- [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] R. Bartnik, The mass of an asymptotically flat manifold, Comm. on Pure and Appl. Math. 39 (1986), 661-693. Zbl0598.53045
- [4] P. B. Gilkey, The geometry of spherical space form groups, Series in Pure Mathematics, vol. 7, World Scientific, Singapore, 1989. Zbl0789.57001
- [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] P. B. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Diff. Geom. 29 (1989), 665-683. Zbl0671.53045
- [7] P. B. Kronheimer, A Torelli-type theorem for gravitational instantons, J. Diff. Geom. 29 (1989), 685-697. Zbl0671.53046
- [8] H. B. Lawson and M.-L. Michelson, Spin geometry, Princeton University Press, Princeton, 1989.
- [9] C. LeBrun, Counterexamples to the generalized positive action conjecture, C.M.P. 118 (1988), 591-596. Zbl0659.53050
- [10] M.Y. Wang, Parallel spinors and parallel forms, Ann. Global Anal. Geom. 7 (1989), 59-68. Zbl0688.53007
- [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] E. Witten, A new proof of the positive energy theorem, Comm. Math. Phys. 80 (1981), 381-402. Zbl1051.83532
- [13] J.A. Wolf, Spaces of constant curvature, McGraw-Hill, 1967. Zbl0162.53304

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