Non-homogeneous fully nonlinear contracting flows of convex hypersurfaces

We consider a general class of non-homogeneous contracting flows of convex hypersurfaces in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> Rⁿ⁺¹ , and prove the existence and regularity of the flow before extincting to a point in finite time.