All Questions
4 questions
22
votes
0
answers
2k
views
Characterising critical points of $E(f)=\int_{M}| \bigwedge^2 df|^2 \text{Vol}_{M}$
$\newcommand{\id}{\operatorname{Id}}$
$\newcommand{\R}{\mathbb{R}}$
$\newcommand{\TM}{\operatorname{TM}}$
$\newcommand{\Hom}{\operatorname{Hom}}$
$\newcommand{\Cof}{\operatorname{Cof}}$
$\newcommand{\...
9
votes
0
answers
289
views
Is there a variational interpretation for the equation $\operatorname{div}(\star \circ \bigwedge^k df\circ \star )=0$?
$\newcommand{\id}{\operatorname{Id}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\TM}{\operatorname{TM}}
\newcommand{\Hom}{\operatorname{Hom}}
\newcommand{\Cof}{\operatorname{Cof}}
\newcommand{\Det}{\...
3
votes
0
answers
72
views
Compactness of bounded index solutions of the Yamabe problem
Consider, a closed Riemannian manifold $ (M^n,g) $ , $ n \geq 3 $, with positive Yamabe invariant: $$ 0< Y(M, [g]):= \inf_{0<v \in H^1} Q_g(v), $$ where $$ Q_g(v) = \inf_{0 <v \in H^1} \...
1
vote
0
answers
62
views
A particular semi-linear equation on Riemannian manifolds
Let $m\in \mathbb{N}\setminus \{1\}$ and suppose $(M,g)$ denotes a compact smooth Riemannian manifold with smooth boundary and consider the semi-linear equation
$$-\Delta_g u+q(x)u + a(x)u^m=0\quad \...