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22 votes
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Characterising critical points of $E(f)=\int_{M}| \bigwedge^2 df|^2 \text{Vol}_{M}$

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Asaf Shachar's user avatar
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9 votes
0 answers
289 views

Is there a variational interpretation for the equation $\operatorname{div}(\star \circ \bigwedge^k df\circ \star )=0$?

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Asaf Shachar's user avatar
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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} \...
Marc's user avatar
  • 457
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 \...
Ali's user avatar
  • 4,135