arXiv subjects
Publications and source records attributed to Sun-Chin Chu.
Type II (ancient) solutions to the Ricci flow on surfaces are not yet classified. It is conjectured that the Rosenau solution and the cigar are the only solutions, modulo scaling. In this paper, we mainly study the backward limit and the circumference at spatial infinity of Type II ancient solutions on noncompact surfaces.
We mainly study 3-dimensional complete gradient Ricci solitons with positive sectional curvature, whose scalar curvature attains its maximum at some point. In section 2, we estimate the area growth of level sets and the volume growth of sublevel sets of a Ricci potential. In section 3, we show that the scalar curvature of such solitons approaches zero at infinity. In section 4, we investigate the geometry of such solitons at infinity, e.g., the tangent cone, the asymptotic behavior, etc.
We give a geometric interpretation of Hamilton's matrix Harnack inequality for the Ricci flow as the curvature of a connection on space-time.
We give a geometric interpretation of the linear trace Harnack inequality for the Ricci flow.