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Abstract There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type and . Gravitational instantons of type were previously classified by Chen–Chen. In this paper, we prove a classification theorem for gravitational instantons. We determine the topology and prove existence of “uniform” coordinates at infinity for both ALG and gravitational instantons. We also prove a result regarding the relationship between ALG gravitational instantons of order and those of order 2.
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This content will become publicly available on April 1, 2026
Classification of solutions to an elliptic equation on $\mathbb R^2$ with nonlocal nonlinearity
A semilinear elliptic equation on $$\mathbb R^2$$ having nonlocal nonlinearity of Choquard type is considered. The entire solutions to the equation under consideration are classified under integrability assumptions that are invariant under the natural symmetries of the problem. This classification theorem can be viewed as an extension of the classification theorem of W. Chen and C. Li for the classical Liouville equation in the sense that, as the nonlocality vanishes, the classification result in the present work is consistent with that of Chen and Li.
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- Award ID(s):
- 2418889
- PAR ID:
- 10587795
- Publisher / Repository:
- American Institute of Mathematical Sciences
- Date Published:
- Journal Name:
- Discrete and Continuous Dynamical Systems
- Volume:
- 0
- Issue:
- 0
- ISSN:
- 1078-0947
- Page Range / eLocation ID:
- 0 to 0
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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