On Convexity in Product of Riemannian Manifolds

[1] M. Beltagy. Immersions into manifolds without conjugate points. PhD thesis, University of
Durham, England, 1982.
[2] M. Beltagy. On the geometry of the cartesian product of manifolds. Bulletin of the Calcutta
Mathematical Society, 81(4):315–320, 1989.
[3] M. Beltagy. Convex and starshaped subset in manifolds product. Communications Faculty
of Sciences University of Ankara Series A, 41(1-2):35–44, 1992.
[4] M. Beltagy. Sufficient conditions for convexity in manifolds without focal points. Com-
mentationes Mathematicae Universitatis Carolinae, 34(3):443–449, 1993.
[5] M. Beltagy and A. El-Araby. Convexity in special types of riemannian manifolds. Bulletin
of the Calcutta Mathematical Society, 94(3):153–162, 2002.
[6] M. Beltagy and A. El-Araby. Starshaped sets in riemannian manifolds without conjugate
points. Far East Journal of Mathematical Sciences, 6(2):187–196, 2002.
REFERENCES 63
[7] V. Boltyanski, H. Martini, and P.S. Soltan. Excursions into Combinatorial Geometry.
Springer, Berlin, Germany, 1997.
[8] L. Danzer, B. Grünbaum, and V. Klee. Helly’s theorem and its relatives. American Mathematical
Society, Providence, RI, 1963.
[9] R. J. Dwilewicz. A short history of convexity. Differential Geometry - Dynamical Systems,
11:112–129, 2009.
[10] S. Hosseini and M. Pouryayevali. On the metric projection onto prox-regular subsets of
riemannian manifolds. Proceedings of the American Mathematical Society, 141(1):233–
244, 2013.
[11] M. A. Jiménez, G. R. Garzón, and A. R. Lizana. Optimality Conditions in Vector Optimiza-
tion. Bentham Science Publishers, 2010.
[12] A. Kiliçman and W Saleh. A note on starshaped sets in2-dimensional manifolds without
conjugate points. Journal of Function Spaces, 2014:Article ID 675735, 3 pages, 2014.
[13] H. Martini and K. Swanepoel. Generalized convexity notions and combinatorial geometry.
Congressus Numerantium, 164:65–93, 2003.
[14] H. Martini and K.J. Swanepoel. The geometry of minkowski spaces-a survey. part ii.
Expositiones mathematicae, 22(2):93–144, 2004.
[15] H.B. Pandey. Cartesian product of two manifolds. Indian Journal of Pure and Applied
Mathematics, 12(1):55–60, 1981.
[16] W. Saleh and A. Kiliçman. On generalized s-convex functions on fractal sets. JP Journal
of Geometry and Topology, 17(1):63–82, 2015.
[17] G. Santhanam. Isoperimetric upper bounds for the first eigenvalue. Proceedings-
Mathematical Sciences, 122(3):375–384, 2012.
[18] C. Udriste. Convex functions and optimization methods on Riemannian manifolds, volume
297. Springer Science & Business Media, 1994.
[19] F. M. Valentine. Convex Subsets. McGraw-Hill Series Higher Math., McGraw-Hill, New
York, 1964.