Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On subelliptic harmonic maps with potential   Let $(M,H,g_H;g)$ be a sub-Riemannian manifold and $(N,h)$ be a Riemannian
manifold. For a smooth map $u: M \to N$, we consider the energy functional
$E_G(u) = \frac{1}{2} \int_M[|\mathrm{d}u_H|^2-2G(u)] \mathrm{d}V_M$, where
$\mathrm{d}u_H$ is the horizontal differential of $u$, $G:N\to \mathbb{R}$ is a
smooth function on $N$. The critical maps of $E_G(u)$ are referred to as
subelliptic harmonic maps with potential $G$. In this paper, we investigate the
existence problem for subelliptic harmonic maps with potentials by a
subelliptic heat flow. Assuming that the target Riemannian manifold has
non-positive sectional curvature and the potential $G$ satisfies various
suitable conditions, we prove some Eells-Sampson type existence results when
the source manifold is either a step-$2$ sub-Riemannian manifold or a step-$r$
sub-Riemannian manifold whose sub-Riemannian structure comes from a tense
Riemannian foliation.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga