Half-space theorems for translating solitons of the r-mean curvature flow
Abstrak
In this paper, we establish nonexistence results for complete translating solitons of the r-mean curvature flow under suitable growth conditions on the (r-1)-mean curvature and on the norm of the second fundamental form. We first show that such solitons cannot be entirely contained in the complement of a right rotational cone whose axis of symmetry is aligned with the translation direction. We then relax the growth condition on the (r-1)-mean curvature and prove that properly immersed translating solitons cannot be confined to certain half-spaces opposite to the translation direction. We conclude the paper by showing that complete, properly immersed translating solitons satisfying appropriate growth conditions on the (r-1)-mean curvature cannot lie completely within the intersection of two transversal vertical half-spaces.
Penulis (3)
Hilário Alencar
G. Pacelli Bessa
Gregório Silva Neto
Akses Cepat
- Tahun Terbit
- 2026
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓