‎Based on a definition for circle in Finsler space‎, ‎recently proposed by one of the present authors and Z‎. ‎Shen‎, ‎a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

Port-wine stain is a vascular malformation characterized pathologically by ectasia of superficial dermal capillaris and clinically by persistent macular erythema. The association of a port-wine stain on a limb with soft tissue swelling, with or without bony overgrowth, is termed klippel-Trenaunay syndrome. Phakomatosis pigmento-vascularis is a combination of port-wine stain and cutaneous ...