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On Bonnesen-Style Symmetric Mixed Isohomothetic Inequality In ℝ2
In this paper, we investigate the translative containment measure for a convex domain K i to contain, or to be contained in the homothetic copy of...
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A sharp reverse Bonnesen-style inequality and generalization
We investigate the isoperimetric deficit of the oval domain in the Euclidean plane. Via the kinematic formulae of Poincaré and Blaschke, and...
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A Faber-Krahn inequality for mixed local and nonlocal operators
We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator and we establish a quantitative Faber-Krahn...
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The Relative Positive Center Set and Its Geometric Applications
In this paper, the relative positive center set of convex plane curves is introduced and described. As its applications, some geometric inequalities...
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Geometry in the Twentieth Century: A Return to Euclid – The Work of Herbert Busemann
This is an exposition of the work of Herbert Busemann (1905–1994), seen as a return to the geometry of Ancient Greece. The importance of this work,...
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Bonnesen-style Wulff isoperimetric inequality
The Wulff isoperimetric inequality is a natural extension of the classical isoperimetric inequality (Green and Osher in Asian J. Math. 3:659-676
1999 )... -
Geometry in the Twentieth Century: A Return to Euclid – The Work of Herbert Busemann
This is an exposition of the work of Herbert Busemann (1905–1994), seen as a return to the geometry of Ancient Greece. The importance of this work,...
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On a Class of Generalized Curve Flows for Planar Convex Curves
In this paper, the authors consider a class of generalized curve flow for convex curves in the plane. They show that either the maximal existence...
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On a Logarithmic Type Nonlocal Plane Curve Flow
In this paper the author devotes to studying a logarithmic type nonlocal plane curve flow. Along this flow, the convexity of evolving curve is...
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Integralgeometrie
Die interessantesten mathematischen Probleme sind i. Allg. diejenigen, die man verhältnismäßig einfach formulieren kann, die vielfältige...
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A Path in History, from Curvature to Convexity
We describe a path in the history of curvature, starting from Greek antiquity, in the works of Euclid, Apollonius, Archimedes and a few others,...
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A reverse isoperimetric inequality for embedded starshaped plane curves
In this note, we present a reverse isoperimetric inequality for embedded starshaped closed plane curves, which states that if K is a starshaped...
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Starshaped sets
This is an expository paper about the fundamental mathematical notion of starshapedness, emphasizing the geometric, analytical, combinatorial, and...
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Translative containment measure and symmetric mixed isohomothetic inequalities
We first investigate the translative containment measure for convex domain K 0 to contain, or to be contained in, the homothetic copy of another...
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Bonnesen-Style Symmetric Mixed Isoperimetric Inequality
For convex domains K i (i = 0, 1) (compact convex sets with non-empty interiors) in the Euclidean...
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