# Some nonexistence theorems on stable minimal submanifolds

Colloquium Mathematicae (1997)

- Volume: 73, Issue: 1, page 1-13
- ISSN: 0010-1354

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topLi, Haizhong. "Some nonexistence theorems on stable minimal submanifolds." Colloquium Mathematicae 73.1 (1997): 1-13. <http://eudml.org/doc/210476>.

@article{Li1997,

abstract = {We prove that there exist no stable minimal submanifolds in some n-dimensional ellipsoids, which generalizes J. Simons' result about the unit sphere and gives a partial answer to Lawson–Simons' conjecture.},

author = {Li, Haizhong},

journal = {Colloquium Mathematicae},

keywords = {stable minimal submanifolds; curvature pinching; stable -currents},

language = {eng},

number = {1},

pages = {1-13},

title = {Some nonexistence theorems on stable minimal submanifolds},

url = {http://eudml.org/doc/210476},

volume = {73},

year = {1997},

}

TY - JOUR

AU - Li, Haizhong

TI - Some nonexistence theorems on stable minimal submanifolds

JO - Colloquium Mathematicae

PY - 1997

VL - 73

IS - 1

SP - 1

EP - 13

AB - We prove that there exist no stable minimal submanifolds in some n-dimensional ellipsoids, which generalizes J. Simons' result about the unit sphere and gives a partial answer to Lawson–Simons' conjecture.

LA - eng

KW - stable minimal submanifolds; curvature pinching; stable -currents

UR - http://eudml.org/doc/210476

ER -

## References

top- [FF] H. Federer and W. Fleming, Normal and integral currents, Ann. of Math. 72 (1960), 458-520. Zbl0187.31301
- [LS] H. B. Lawson Jr. and J. Simons, On stable currents and their applications in real and complex projective space, ibid. 98 (1973), 427-450.
- [L1] P. F. Leung, Minimal submanifolds in a sphere, Math. Z. 183 (1983), 75-86. Zbl0491.53045
- [L2] P. F. Leung, An estimate on the Ricci curvature on a submanifold and some applications, Proc. Amer. Math. Soc. 114 (1992), 1051-1061. Zbl0753.53003
- [M] H. Mori, Notes on stable currents, Pacific J. Math. 61 (1975), 235-240. Zbl0329.49030
- [O] Y. Ohnita, Stable minimal submanifolds in compact rank one symmetric spaces, Tôhoku Math. J. 38 (1986), 199-217. Zbl0594.53037
- [PS] Y. L. Pan and Y. B. Shen, Stability of harmonic maps and minimal immersions, Proc. Amer. Math. Soc. 93 (1985), 111-117. Zbl0527.58010
- [S] J. Simons, Minimal varieties in riemannian manifolds, Ann. of Math. 88 (1968), 62-105. Zbl0181.49702

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