We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε via the containment measure of a convex domain to con...We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style inequalities that extend the known Bottema＇s result in the Euclidean plane E2.展开更多
Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact em...Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger＇s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.展开更多
Weak log-Sobolev and Lp weak Poincare inequalities for general symmetric forms are investigated by using newly defined Cheeger＇s isoperimetric constants. Some concrete examples of ergodic birth-death processes are al...Weak log-Sobolev and Lp weak Poincare inequalities for general symmetric forms are investigated by using newly defined Cheeger＇s isoperimetric constants. Some concrete examples of ergodic birth-death processes are also presented to illustrate the results.展开更多
In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an...In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an analogue of the known Bottema's result of 1933 in the Euclidean plane E2.展开更多
Ⅰ. INTRODUCTIONSuppose Ω is a convex domain with piecewise smooth boundary on a 2-dimensional sphere with radius R. Let λ<sub>1</sub>（Ω）be the first eigenvalue of the Laplacian with
基金supported by National Natural Science Foundation of China (Grant Nos.10971167, 11271302 and 11101336)
文摘We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style inequalities that extend the known Bottema＇s result in the Euclidean plane E2.
基金Supported in part by Program for New Century Excellent Talents in University (NCET)973 Project (Grant No.2006CB805901)National Natural Science Foundation of China (Grant No.10721091)
文摘Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger＇s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.
文摘Weak log-Sobolev and Lp weak Poincare inequalities for general symmetric forms are investigated by using newly defined Cheeger＇s isoperimetric constants. Some concrete examples of ergodic birth-death processes are also presented to illustrate the results.
基金supported in part by National Natural Science Foundation of China (Grant No.10971167)
文摘In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an analogue of the known Bottema's result of 1933 in the Euclidean plane E2.
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTIONSuppose Ω is a convex domain with piecewise smooth boundary on a 2-dimensional sphere with radius R. Let λ<sub>1</sub>（Ω）be the first eigenvalue of the Laplacian with
