The existence of strong solution for a class of fully nonlinear equation

2019 ◽  
Vol 43 (4) ◽  
pp. 1530-1542
Author(s):  
Ruili Wu
Keyword(s):  
Nonlinear Equation ◽  
Strong Solution ◽  
Fully Nonlinear ◽  
Fully Nonlinear Equation

scholarly journals The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1

2008 ◽  
Vol 80 (1) ◽  
pp. 3-19
Author(s):  
Shuguo Shi
Keyword(s):  
Nonlinear Equation ◽  
Representation Formula ◽  
Gauss Map ◽  
Weierstrass Representation ◽  
Fully Nonlinear ◽  
Duality Property ◽  
Fully Nonlinear Equation ◽  
Monge Ampere

In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1. Particularly, we discuss the surfaces with conformal normal Gauss map in H³ and S³1, and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S³1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S³1. Some examples of surfaces in S³1 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère type for the graphs in S³1 with conformal normal Gauss map is derived.

scholarly journals A fully nonlinear equation for the flame front in a quasi-steady combustion model

2010 ◽  
Vol 27 (4) ◽  
pp. 1415-1446 ◽  
Author(s):  
Claude-Michel Brauner ◽  
◽  
Josephus Hulshof ◽  
Luca Lorenzi ◽  
Gregory I. Sivashinsky ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Flame Front ◽  
Combustion Model ◽  
Fully Nonlinear ◽  
Steady Combustion ◽  
Fully Nonlinear Equation

An a priori estimate for a fully nonlinear equation on four-manifolds

2002 ◽  
Vol 87 (1) ◽  
pp. 151-186 ◽  
Author(s):  
Sun-Yung A. Chang ◽  
Matthew J. Gursky ◽  
Paul Yang
Keyword(s):  
Nonlinear Equation ◽  
A Priori ◽  
A Priori Estimate ◽  
Priori Estimate ◽  
Fully Nonlinear ◽  
Four Manifolds ◽  
Fully Nonlinear Equation

scholarly journals A fully nonlinear equation in relativistic Teichmüller theory

2019 ◽  
Vol 30 (13) ◽  
pp. 1940004
Author(s):  
Luen-Fai Tam ◽  
Tom Yau-Heng Wan
Keyword(s):  
Nonlinear Equation ◽  
Teichmüller Space ◽  
Type Equation ◽  
Teichmuller Space ◽  
Teichmuller Theory ◽  
Dimension Formula ◽  
Teichmüller Theory ◽  
Genus Formula ◽  
Fully Nonlinear Equation ◽  
Monge Ampere

We obtain some basic estimates for a Monge–Ampère type equation introduced by Moncrief in the study of the Relativistic Teichmüller Theory. We then give another proof of the parametrization of the Teichmüller space obtained by Moncrief. Our approach provides yet another proof of the classical Teichmüller theorem that the Teichmüller space of a compact oriented surface of genus [Formula: see text] is diffeomorphic to the disk of dimension [Formula: see text]. We also give another proof of properness of a certain energy function on the Teichmüller space.

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