Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic finiteness of minimal surfaces with bounded Morse index   Given a compact 3-manifold N without boundary, we prove that for a bumpy
metric of positive scalar curvature the space of minimal surfaces having a
uniform upper bound on the Morse index is always finite unless the manifold
itself contains an embedded minimal RP^2. In particular, we derive a generic
finiteness result whenever N does not contain a copy of RP^3 in its prime
decomposition. We discuss the obstructions to any further generalization of
such a result. When the metric g is required to be (scalar positive and)
strongly bumpy (meaning that all closed, immersed minimal surfaces do not have
Jacobi fields, a notion recently proved to be generic by B. White) the same
conclusion holds true for any closed 3-manifold.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ