The quermassintegral inequalities for k-convex starshaped domains

By Pengfei Guan, Junfang Li. 2009

221 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/53dad5585e4d34e4740187505662309b8f4ba537

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In Applied Mathematics

1. Emanuel Milman
2. Guofang Wang
3. A. V. Kolesnikov
4. Chao Xia
5. Junfang Li
6. Julian Scheuer
7. M. Makowski
8. Jie Wu

In Geometry and Topology

1. A. V. Kolesnikov
2. Emanuel Milman
3. Guofang Wang
4. Chao Xia
5. Julian Scheuer
6. M. Makowski
7. Jie Wu
8. Yuxin Ge

Citations in the corpus

• Hyperbolic Alexandrov-Fenchel quermassintegral inequalities I (2013, methodology): “See the work of Guan-Li [18], Huisken [21] and Chang-Wang [6].”
• Brascamp–Lieb-Type Inequalities on Weighted Riemannian Manifolds with Boundary (2013, background): “iemannian version of Minkowski’s second inequality was already noted by Reilly [57]. We also mention that in Euclidean space, a related Alexandrov– Fenchel inequality was shown to hold by Guan and Li [22] for arbitrary mean-convex star-shaped domains. 8.2 Riemannian Brunn–Minkowski via Parallel Norm”
• Hyperbolic Alexandrov-Fenchel quermassintegral inequalities II (2013, background): “een intensively studied in the last several decades. See classical books of Santos[39], Burago-Zalgaller [9] and Schneider [41]. For the non-convex domains, see the recent interesting work of Guan-Li [25] and Huisken [31] and also the work of Chang-Wang [11]. Here we just mention a conformal version”
• A Mean Curvature Type Flow in Space Forms (2013, methodology): “The authors used the inverse mean curvature type of flows to prove Alexandrov-Fenchel quermassintegral inequalities for starshaped k-convex domains in [9].”
• A geometric inequality on hypersurface in hyperbolic space (2012, unknown): “[8]) ∂tσm = ∂σm ∂hji ∂th j i”
• Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere (2013, background): “In 2009, Guan and Li (see [15]) used inverse F -curvature flows in Euclidean space to show these inequalities for k-convex, starshaped domains.”
• Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds (2017, methodology): “We also mention that in Euclidean space, a related Alexandrov-Fenchel inequality was shown to hold by Guan and Li [26] for arbitrary mean-convex star-shaped domains.”
• Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space (2013, methodology): “Various flows have been employed to prove geometric inequalities, see for instance [2, 5, 13, 18, 19, 21, 24, 25, 26, 29, 30, 31, 38].”