Boundary regularity and stability for spaces with Ricci bounded below
Boundary regularity and stability for spaces with Ricci bounded below
Abstract This paper studies the structure and stability of boundaries in noncollapsed $${{\,\mathrm{RCD}\,}}(K,N)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mspace /> <mml:mi>RCD</mml:mi> <mml:mspace /> </mml:mrow> <mml:mo>(</mml:mo> <mml:mi>K</mml:mi> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> spaces, that is, metric-measure spaces $$(X,{\mathsf {d}},{\mathscr {H}}^N)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> …