»ã±¨±êÌâ (Title)£º A Liouville theorem for the affine maximal equation on half-space

ÖÐÎıêÌ⣺°ë¿Õ¼äÉÏ·ÂÉ伫·çÑų̵ÄLiouville¶¨Àí

»ã±¨ÈË (Speaker)£ºÖܱ󣨱±¾©´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê1ÔÂ17ÈÕ(ÖÜÈý) 17:00-18:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

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»ã±¨ÌáÒª£ºThe famous affine Bernstein theorem, also called Chern¡¯s conjecture, asserts that an affine maximal graph of a smooth, locally uniformly convex function on Euclidean space is a paraboloid. This conjecture was first proved by Trudinger-Wang in dimension two in 2000. One can easily find affine maximal graphs which are not paraboloid on half spaces. In this talk, we show a Liouville theorem for the affine maximal equation on half-spaces with certain assumptions. The proof is based on the study on the related linearized Monge-Amp\`ere equation and the Monge-Amp\`ere equation