TL;DR
This paper discusses the existence of solutions for various geometric partial differential equations, exploring examples, principles, inequalities, and related mathematical concepts in the field.
Contribution
It provides specific examples and remarks on the existence of solutions for geometric PDEs, along with insights into related principles and inequalities.
Findings
Examples of solutions for Yamabe and scalar curvature equations
Remarks on maximum principles and Green functions
Discussion of inequalities like Sobolev and Moser-Trudinger
Abstract
We give some examples of the existence of solutions of geometric PDEs (Yamabe equation, Prescribed Scalar Curvature Equation, Gaussian curvature). We also give some remarks on second order PDE and Green functions and on the maximum principles. And on Harnack type inequalities and Sobolev and interpolation inequality and Moser-Trudinger inequality. And some remarks on the equations.
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