Ruled Surfaces of Generalized Self-Similar Solutions of the Mean Curvature Flow
Ruled Surfaces of Generalized Self-Similar Solutions of the Mean Curvature Flow
Abstract In Euclidean space, we investigate surfaces whose mean curvature H satisfies the equation $$H=\alpha \langle N,{\mathbf {x}}\rangle +\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>=</mml:mo> <mml:mi>α</mml:mi> <mml:mo>⟨</mml:mo> <mml:mi>N</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo>⟩</mml:mo> <mml:mo>+</mml:mo> <mml:mi>λ</mml:mi> </mml:mrow> </mml:math> , where N is the Gauss map, $${\mathbf {x}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>x</mml:mi> </mml:math> is the …