A compactness result for Fano manifolds and K\"ahler Ricci flows

We obtain a compactness result for Fano manifolds and K\"ahler Ricci flows. Comparing to the more general Riemannian versions by Anderson and Hamilton, in this Fano case, the curvature assumption is much weaker and is preserved by the K\"ahler Ricci flows. One assumption is the boundedness of the Ricci potential and the other is the smallness of Perelman's entropy. As one application, we obtain a new local regularity criteria and structure result for K\"ahler Ricci flows. The proof is based on a H\"older estimate for the gradient of harmonic functions, which may be of independent interest

Isoperimetric inequality under K\"ahler Ricci flow

Let ({\M}, g(t)) be a K\"ahler Ricci flow with positive first Chern class. We prove a uniform isoperimetric inequality for all time. In the process we also prove a Cheng-Yau type log gradient bound for positive harmonic functions on ({\M}, g(t)), and a Poincar\'e inequality without assuming the Ricci curvature is bounded from below.Comment: final version, to appear in Am. J. Mat

Person Transfer GAN to Bridge Domain Gap for Person Re-Identification

Although the performance of person Re-Identification (ReID) has been significantly boosted, many challenging issues in real scenarios have not been fully investigated, e.g., the complex scenes and lighting variations, viewpoint and pose changes, and the large number of identities in a camera network. To facilitate the research towards conquering those issues, this paper contributes a new dataset called MSMT17 with many important features, e.g., 1) the raw videos are taken by an 15-camera network deployed in both indoor and outdoor scenes, 2) the videos cover a long period of time and present complex lighting variations, and 3) it contains currently the largest number of annotated identities, i.e., 4,101 identities and 126,441 bounding boxes. We also observe that, domain gap commonly exists between datasets, which essentially causes severe performance drop when training and testing on different datasets. This results in that available training data cannot be effectively leveraged for new testing domains. To relieve the expensive costs of annotating new training samples, we propose a Person Transfer Generative Adversarial Network (PTGAN) to bridge the domain gap. Comprehensive experiments show that the domain gap could be substantially narrowed-down by the PTGAN.Comment: 10 pages, 9 figures; accepted in CVPR 201