A variant prescribed curvature flow on closed surfaces with negative Euler characteristic
A variant prescribed curvature flow on closed surfaces with negative Euler characteristic
Abstract On a closed Riemannian surface $$(M,{\bar{g}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo>,</mml:mo> <mml:mover> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> with negative Euler characteristic, we study the problem of finding conformal metrics with prescribed volume $$A>0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and the …