Geometric Partial Differential Equations from Unified String Theories

2019/06/09 by D. H. Phong, Duong H. Phong, Phong, Duong H. · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.AP #math.CV

paper · pdf · doi:10.48550/arxiv.1906.03693

Contribution to the Proceedings of the ICCM 2018, Taipei, Taiwan, 22 pages

arxiv created 2019/06/09 · openalex publication_date 2019/06/09 · arxiv updated 2019/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An informal introduction to some new geometric partial differential equations motivated by string theories is provided. Some of these equations are also interesting from the point of view of non-Kähler geometry and the theory of non-linear partial differential equations. In particular, a survey is given of joint works of the author with Teng Fei, Bin Guo, Sebastien Picard, and Xiangwen Zhang.

Citations

• Laplacian Flow for Closed G₂-Structures: Short Time Behavior
• On the parabolic kernel of the Schrödinger operator
• Fu-Yau Hessian Equations

Cited by

• The canonical symmetry reduction of string backgrounds

Related

• Differential Equations in Special Kahler Geometry
• Theory of characteristics for first order partial differential equations
• Geometry and nonlinear analysis
• Geometric Methods in Partial Differential Equations
• Algebraic Approaches to Partial Differential Equations