# Rigidity of spherical product Ricci solitons

@inproceedings{Sun2021RigidityOS, title={Rigidity of spherical product Ricci solitons}, author={Ao Sun and Jonathan J. Zhu}, year={2021} }

We show that S × S is isolated as a shrinking Ricci soliton in the space of metrics, up to scaling and diffeomorphism. We also prove the same rigidity for S × N , where N belongs to a certain class of closed Einstein manifolds. These results are the Ricci flow analogues of our results for Clifford-type shrinking solitons for the mean curvature flow.

## One Citation

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## References

SHOWING 1-10 OF 32 REFERENCES

### Rigidity and Infinitesimal Deformability of Ricci Solitons

- Mathematics
- 2016

In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex…

### Compactness theory of the space of Super Ricci flows

- Mathematics
- 2020

We develop a compactness theory for super Ricci flows. Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an appropriate sense subsequentially converges…

### The moduli space of Fano manifolds with Kähler–Ricci solitons

- MathematicsAdvances in Mathematics
- 2019

### Rigidity and {\L}ojasiewicz inequalities for Clifford self-shrinkers.

- Mathematics
- 2020

We show that the product of two round shrinking spheres is an isolated self-shrinker in any codimension, modulo rotations. Moreover we prove explicit {\L}ojasiewicz inequalities near such products.…

### Stability and instability of Ricci solitons

- Mathematics
- 2015

We consider the volume-normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton $$(M,g)$$(M,g) is a local maximum of Perelman’s shrinker entropy, any…

### Rigidity of generic singularities of mean curvature flow

- Mathematics
- 2013

Shrinkers are special solutions of mean curvature flow (MCF) that evolve by rescaling and model the singularities. While there are infinitely many in each dimension, Colding and Minicozzi II (Ann.…

### Linear stability of Perelman's $ν$-entropy on symmetric spaces of compact type

- Mathematics
- 2013

Following Cao-Hamilton-Ilmanen, in this paper we study the linear stability of Perelman's $\nu$-entropy on Einstein manifolds with positive Ricci curvature. We observe the equivalence between the…

### Singularities of Ricci flow and diffeomorphisms

- Mathematics
- 2021

Comparing and recognizing metrics can be extraordinarily difficult because of the group of diffeomorphisms. Two metrics, that could even be the same, could look completely different in different…