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In undergoing this life, many people always try to do and get the best. New knowledge, experience, lesson, and everything that can improve the life will be done. However, many people sometimes feel confused to get those things. Feeling the limited of experience and sources to be better is one of the lacks to own. However, there is a very simple thing that… (More)

- BY J. L. BARBOSA, M. DO CARMO, J. L. BARBOSA
- 2007

Let M<=R be a minimal surface. A domain Z><= M is an open connected set with compact closure D and such that its boundary dD is a finite union of piecewise smooth curves. We say that D is stable if D is a minimum for the area function of the induced metric, for all variations of D which keep dD fixed. In this note we announce the following estimate of the… (More)

- Manfredo P. do Carmo
- Vieweg Studium Aufbaukurs Mathematik
- 1998

Let M be a compact (two-sided) minimal hypersurface in a Riemannian manifold M n+1 . It is a simple fact that if M has positive Ricci curvature then M cannot be stable (i. e. its Jacobi operator L has index at least one). If M = S(1) is the unit sphere and L has index one, then it is known that M must be a totally geodesic equator. We prove that if M is the… (More)

- Manfredo P. do Canno, Manfredo P. do Carmo
- 2010

The last ten years have seen an intense activity on certain questions that arise in connection with the study of minimal surfaces. Among such questions one should mention those of regularity, embeddability, stability and finiteness of the number of minimal surfaces spanning a given boundary. In this lecture I would like to describe a few ideas, results and… (More)

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