4.6 Article

On an inverse curvature flow in two-dimensional space forms

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics

Locally constrained curvature flows and geometric inequalities in hyperbolic space

Yingxiang Hu et al.

Summary: In this paper, the locally constrained curvature flow of hypersurfaces in hyperbolic space is studied. The flow preserves certain properties and leads to sharp geometric inequalities. A new locally constrained curvature flow using the shifted principal curvatures is introduced, and its convergence properties are proved.

MATHEMATISCHE ANNALEN (2022)

Article Mathematics

Alexandrov-Fenchel type inequalities in the sphere

Min Chen et al.

Summary: In this paper, we proved the Alexandrov-Fenchel inequalities for embedded, closed, connected, and convex C-2-hypersurfaces in Sn+1, which states that A(k) >= xi(k,k-2)(A(k-2)) holds for any 1 <= k <= n- 1, with A(k) being the quermassintegral and xi(k,k-2) being a unique positive function that satisfies the equality when M is a geodesic sphere.

ADVANCES IN MATHEMATICS (2022)

Article Mathematics, Applied

Minkowski inequalities and constrained inverse curvature flows in warped spaces

Julian Scheuer

Summary: This paper deals with locally constrained inverse curvature flows in a broad class of Riemannian warped spaces. For a certain class of such flows, long-time existence and smooth convergence to a radial coordinate slice is proven. In the case of two-dimensional surfaces and a suitable speed, these flows exhibit two monotone quantities, resulting in new Minkowski type inequalities. In higher dimensions, new Minkowski inequalities are obtained using the inverse mean curvature flow when the ambient radial Ricci curvature is constantly negative.

ADVANCES IN CALCULUS OF VARIATIONS (2022)

Article Mathematics

Isoperimetric Type Inequalities and Hypersurface Flows

Pengfei Guan et al.

Summary: New types of hypersurface flows have been introduced in order to establish isoperimetric type inequalities in geometry. These flows aim to efficiently solve problems in geometric calculus of variations by using variational structures to develop flows that are monotonic with respect to curvature integrals. This poses interesting yet challenging PDE problems with significant geometric implications.

JOURNAL OF MATHEMATICAL STUDY (2021)

Article Mathematics

Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature

Virginia Agostiniani et al.

INVENTIONES MATHEMATICAE (2020)

Article Mathematics, Applied

Geometric inequalities for hypersurfaces with nonnegative sectional curvature in hyperbolic space

Yingxiang Hu et al.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2019)

Article Mathematics, Applied

A note on expansion of convex plane curves via inverse curvature flow

Heiko Kroener

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS (2019)

Article Mathematics

Curvature flows in the sphere

Claus Gerhardt

JOURNAL OF DIFFERENTIAL GEOMETRY (2017)

Article Mathematics

Inverse curvature flows in hyperbolic space

Claus Gerhardt

JOURNAL OF DIFFERENTIAL GEOMETRY (2017)

Article Mathematics

An Alexandrov-Fenchel-type inequality for hypersurfaces in the sphere

Frederico Girao et al.

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY (2017)

Article Physics, Multidisciplinary

An Alexandrov-Fenchel-Type Inequality in Hyperbolic Space with an Application to a Penrose Inequality

Levi Lopes de Lima et al.

ANNALES HENRI POINCARE (2016)

Article Mathematics, Applied

RIGIDITY RESULTS, INVERSE CURVATURE FLOWS AND ALEXANDROV-FENCHEL TYPE INEQUALITIES IN THE SPHERE

Matthias Makowski et al.

ASIAN JOURNAL OF MATHEMATICS (2016)

Article Mathematics, Applied

A Minkowski Inequality for Hypersurfaces in the Anti-de Sitter-Schwarzschild Manifold

Simon Brendle et al.

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS (2016)

Article Mathematics, Applied

Monotone quantities involving a weighted σk integral along inverse curvature flows

Kwok-Kun Kwong et al.

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS (2015)

Article Mathematics

A Generalization of Reilly's Formula and its Applications to a New Heintze-Karcher Type Inequality

Guohuan Qiu et al.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES (2015)

Article Mathematics

A Mean Curvature Type Flow in Space Forms

Pengfei Guan et al.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES (2015)

Article Mathematics

A geometric inequality on hypersurface in hyperbolic space

Haizhong Li et al.

ADVANCES IN MATHEMATICS (2014)

Article Mathematics

HYPERBOLIC ALEXANDROV-FENCHEL QUERMASSINTEGRAL INEQUALITIES II

Yuxin Ge et al.

JOURNAL OF DIFFERENTIAL GEOMETRY (2014)

Article Mathematics

A NEW MONOTONE QUANTITY ALONG THE INVERSE MEAN CURVATURE FLOW IN Rn

Kwok-Kun Kwong et al.

PACIFIC JOURNAL OF MATHEMATICS (2014)

Article Mathematics

CONSTANT MEAN CURVATURE SURFACES IN WARPED PRODUCT MANIFOLDS

Simon Brendle

PUBLICATIONS MATHEMATIQUES DE L IHES (2013)

Article Mathematics

Curvature bound for curve shortening flow via distance comparison and a direct proof of Grayson's theorem

Ben Andrews et al.

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK (2011)

Article Mathematics

The quermassintegral inequalities for k-convex starshaped domains

Pengfei Guan et al.

ADVANCES IN MATHEMATICS (2009)

Review Mathematics

The inverse mean curvature flow and the Riemannian Penrose Inequality

G Huisken et al.

JOURNAL OF DIFFERENTIAL GEOMETRY (2001)