Upper bounds for the index of minimal surfaces (Q810896)

The author uses a method of \textit{P. Bérard} and \textit{G. Besson} [J. Funct. Anal. 94, No.2, 375-396 (1980; Zbl 0723.53026)] to prove the following: Let f: \(M\to N\) be a minimal immersion of a surface M into an n-dimensional Hadamard manifold N, and let D be a simply connected compact domain in M with piecewise smooth boundary. Then \[ Index(D)\leq \frac{(n-2)e}{4\pi^ 2}area(D)\int_{D}| A|^ 4dM, \] where A is the second fundamental form of E. The author also considers the case where N is a constant curvature Hadamard manifold.