The Fu-Yau equation with negative slope parameter

• 成果类型: Article
• 署名作者: Phong, Duong H.; Picard, Sebastien; Zhang, Xiangwen
• 署名单位: Columbia University; University of California System; University of California Irvine
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0715-z
• 发表日期: 2017
• 页码: 541-576
• 关键词: nonlinear elliptic-equations; complex hessian equations; 2nd-order estimate; WEAK SOLUTIONS; MANIFOLDS

摘要

The Fu-Yau equation is an equation introduced by Fu and Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter . The equation was solved in dimension 2 by Fu and Yau in two successive papers for , and for . In the present paper, we solve the Fu-Yau equation in arbitrary dimension for . To our knowledge, these are the first non-trivial solutions of the Fu-Yau equation in any dimension strictly greater than 2.