Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metrics with $\lambda_1(-\Delta + k R) \geq 0$ and flexibility in the
  Riemannian Penrose Inequality   On a closed manifold, consider the space of all Riemannian metrics for which
-\Delta + kR is positive (nonnegative) definite, where k > 0 and R is the
scalar curvature. This spectral generalization of positive (nonnegative) scalar
curvature arises naturally for different values of k in the study of scalar
curvature in dimension via minimal hypersurfaces, the Yamabe problem, and
Perelman's Ricci flow with surgery. When k=1/2, the space models apparent
horizons in time-symmetric initial data to the Einstein equations. We study
these spaces in unison and generalize Coda Marques's path-connectedness
theorem. Applying this with k=1/2, we compute the Bartnik mass of 3-dimensional
apparent horizons and the Bartnik--Bray mass of their outer-minimizing
generalizations in all dimensions. Our methods also yield efficient
constructions for the scalar-nonnegative fill-in problem.

22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex