This is a preview of subscription content, log in via an institution to check access.
References
H. Alencar andM. Do Carmo, Hypersurfaces of constant mean curvatures with finite index and volume of polynomial growth. Arch. Math.60, 489–493 (1993), Erratum (to appear in the same journal).
C. H. Baikoussis andT. H. Koufogiorgos, Harmonic map into a cone. Arch. Math.40, 372–376 (1983).
R. L.Bishop and R. J.Crittenden, Geometry of Manifolds. New York 1964.
J. Cheeger andD. G. Ebin, Comparison Theorems in Riemannian Geometry. North-Holland Math. Library, Amsterdam 1975.
S. Y. Cheng, Eigenvalue comparison theorems and its geometric applications. Math. Z.143, 289–297 (1975).
L. Coghlan, Y. Itokawa andR. Kosecki, On the solutions to certain Laplace inequalities with applications to geometry of submanifolds. J. Geom. Anal.2, 195–211 (1992).
J.-H. Eschenburg andJ. J. O'Sullivan, Jacobi tensors and Ricci curvature. Math. Ann.252, 1–26 (1980).
L. Jorge andD. Koutroufiotis, An estimate for the curvature of bounded submanifolds. Amer. J. Math.103, 711–725 (1981).
L. Jorge andF. Xavier, An inequality between the exterior diameter and the mean curvature of bounded immersions. Math. Z.178, 77–82 (1981).
S. Markvorsen, A sufficient condition for a compact immersion to be spherical. Math. Z.183, 407–411 (1983).
S. Markvorsen, On the mean exit time from a minimal submanifold. J. Differential Geom.29, 1–8 (1989).
Author information
Authors and Affiliations
Additional information
Supported partially by NNSFC and NSF of Shandong Province.
Rights and permissions
About this article
Cite this article
Zhou, D. Laplace inequalities with geometric applications. Arch. Math 67, 50–58 (1996). https://doi.org/10.1007/BF01196166
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01196166