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Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator
Positive Curvature Operator Shrinking Ricci Solitons
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2015/8/17
In this paper, we first derive several identities on a compact shrinking Ricci
soliton. We then show that a compact gradient shrinking soliton must be
Einstein, if it admits a Riemannian metri...
The H-flow translating solitons in R^3 and R^4
H-flow translating solitons R^3 R^4 Differential Geometry
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2012/4/17
Motivated by Ilmanen's correspondence, we present an explicit solution to the prescribed Hoffman-Osserman Gauss map problem for non-minimal translators to the mean curvature flow in Euclidean 4-space....
Bach-flat gradient steady Ricci solitons
Bach-flat gradient Ricci solitons Differential Geometry
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2011/9/19
Abstract: In this paper we prove that any $n$-dimensional ($n\ge 4$) complete Bach-flat gradient steady Ricci solitons with positive Ricci curvature is isometric to the Bryant soliton. We also show th...
A note on compact gradient Yamabe solitons
compact gradient Yamabe soliton Yamabe flow constant scalar curvature metric
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2011/9/15
Abstract: We will give a simple proof that the metric of any compact Yamabe gradient soliton (M,g) is a metric of constant scalar curvature when the dimension of the manifold n>2.
Some geometric analysis on generic Ricci solitons
Ricci solitons X–Laplacian scalar curvature estimates maximum principles volume estimates
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2011/9/6
Abstract: We study the geometry of complete generic Ricci solitons with the aid of some geometric-analytical tools extending techniques of the usual Riemannian setting.
On the Geometry of complete Ricci Solitons
Geometry complete Ricci Solitons
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2010/12/1
In this paper we establish three basic equations for a general soliton structure on the Riemannian manifold (M, h , i). We then draw some geometric conclusions with the aid of the maximum principle.
Mach reflection and KP solitons in shallow water
Mach reflection KP solitons shallow water
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2010/4/6
Reflection of an obliquely incident solitary wave onto a vertical wall is studied analytically and experimentally. We use the Kadomtsev-Petviashivili (KP) equation to analyze the evolution and its asy...