Complete classification of nontrivial non-flat two- and three-dimensional complete gradient Yamabe solitons.
Rotational symmetry of complete shrinking gradient Yamabe solitons
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this paper, we show that any nontrivial complete shrinking gradient Yamabe soliton whose scalar curvature is bounded below by the soliton constant everywhere and is strictly greater than the constant at some point is rotationally symmetric. This assumption is optimal for higher dimensions. This result resolves the Yamabe-soliton analogue of Perelman's conjecture.
fields
math.DG 2years
2024 2verdicts
UNVERDICTED 2representative citing papers
Complete classification of nontrivial complete expanding gradient Yamabe solitons when scalar curvature exceeds or falls below the soliton constant.
citing papers explorer
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Classification of low-dimensional complete gradient Yamabe solitons
Complete classification of nontrivial non-flat two- and three-dimensional complete gradient Yamabe solitons.
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Triviality, Rotational Symmetry, and Classification of Complete Expanding Gradient Yamabe Solitons
Complete classification of nontrivial complete expanding gradient Yamabe solitons when scalar curvature exceeds or falls below the soliton constant.