Geodesic
Minimization of the functionals generating curvature operators
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 21, Tome 182 (1990), pp. 29-37 
N. M. Ivochkina. Minimization of the functionals generating curvature operators. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 21, Tome 182 (1990), pp. 29-37. http://geodesic.mathdoc.fr/item/ZNSL_1990_182_a1/
@article{ZNSL_1990_182_a1,
     author = {N. M. Ivochkina},
     title = {Minimization of the functionals generating curvature operators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {29--37},
     year = {1990},
     volume = {182},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_182_a1/}
}
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The paper concerns putting up the variational problems for functionals connected with $m$-curvature operators. The theorems of minimizer's existence are proved.