Profile directory About Mobile apps
Log in Sign up
arXiv Math @arxiv_math@qoto.org
Follow

Liouville Theorem with Boundary Conditions from Chern--Gauss--Bonnet Formula https://arxiv.org/abs/2410.16384 #mathAP #mathDG

Liouville Theorem with Boundary Conditions from Chern--Gauss--Bonnet Formula

The $σ_k(A_g)$ curvature and the boundary $\mathcal{B}^k_g$ curvature arise naturally from the Chern--Gauss--Bonnet formula for manifolds with boundary. In this paper, we prove a Liouville theorem for the equation $σ_k(A_g)=1$ in $\overline{\mathbb{R}^n_+}$ with the boundary condition $\mathcal{B}^k_g=c$ on $\partial\mathbb{R}^n_+$, where $g=e^{2v}|dx|^2$ and $c$ is some nonnegative constant. This extends an earlier result of Wei, which assumes the existence of $\lim_{|x|\to\infty}(v(x)+2\log|x|)$. In addition, we establish a local gradient estimate for solutions of such equations, assuming an upper bound on the solution $v$.

arXiv.org
October 24, 2024 at 3:10 AM · · feed2toot · 0 · 0 · 0
Sign in to participate in the conversation
Qoto Mastodon

QOTO: Question Others to Teach Ourselves
An inclusive, Academic Freedom, instance
All cultures welcome.
Hate speech and harassment strictly forbidden.

Trending now

#news0 people talking
0
#monsterdon0 people talking
0
#ai0 people talking
0

Resources

  • Terms of service
  • Privacy policy

Developers

  • Documentation
  • API

What is Mastodon?

qoto.org

  • About
  • v3.5.19-qoto

More…

  • Source code
  • Mobile apps
v3.5.19-qoto · Privacy policy