Some nonexistence theorems on stable minimal submanifolds

• Autorzy: Haizhong Li
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1997
• Tom: 73
• Numer: 1
• Strony: 1-13

Daty

wydano

1997

otrzymano

1996-01-03

Twórcy

autor

Haizhong Li

• Department of Applied Mathematics Tsinghua University Beijing, 100084 People's Republic of China

Bibliografia

• [FF] H. Federer and W. Fleming, Normal and integral currents, Ann. of Math. 72 (1960), 458-520.
• [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.
• [L2] P. F. Leung, An estimate on the Ricci curvature on a submanifold and some applications, Proc. Amer. Math. Soc. 114 (1992), 1051-1061.
• [M] H. Mori, Notes on stable currents, Pacific J. Math. 61 (1975), 235-240.
• [O] Y. Ohnita, Stable minimal submanifolds in compact rank one symmetric spaces, Tôhoku Math. J. 38 (1986), 199-217.
• [PS] Y. L. Pan and Y. B. Shen, Stability of harmonic maps and minimal immersions, Proc. Amer. Math. Soc. 93 (1985), 111-117.
• [S] J. Simons, Minimal varieties in riemannian manifolds, Ann. of Math. 88 (1968), 62-105.