“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 16958
School of Mathematics
  Title:   Characterization of convex and generalized convex vector fields on Riemannian manifolds
  Author(s):  Elham Ghahraei
  Status:   Published
  Journal: Bull. Iranian Math. Soc.
  Year:  2022
  Pages:   DOI: 10.1007/s41980-022-00684-1
  Supported by:  IPM
  Abstract:
In this paper, we define the concepts of C-convexity and generalized C-convexity of vector fields on Riemannian manifolds and we prove that a locally bounded C-convex vector field on Riemannian manifolds is locally Lipschitz. A new definition of subdifferential of a C-convex vector field is introduced and some of its properties similar to those in the scalar case are shown. The inclusive relations between Clarke generalized Jacobian and Mordukhovich coderivative and this subdifferential are proved. Moreover, the C-convexity and C-quasiconvexity of a vector field and the C-monotonicity and C-quasimonotonicity of its Mordukhovich coderivative are studied. We also present a second-order characterization of C-convex vector fields on Riemannian manifolds.

Download TeX format
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right