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Concepts of almost periodicity and ergodic theorems in locally convex spaces
We wish to investigate mean ergodic theorems for generalizations of almost periodic functions on semigroups, as well as for semigroups of operators...
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On a convexity property of the space of almost fuchsian immersions
We study the space of Hopf differentials of almost fuchsian minimal immersions of compact Riemann surfaces. We show that the extrinsic curvature of...
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Prescribing the gauss curvature of convex bodies in hyperbolic space
The Gauss curvature measure of a pointed Euclidean convex body is a measure on the unit sphere which extends the notion of Gauss curvature to...
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The Parameterized Complexity of Guarding Almost Convex Polygons
The Art Gallery problem is a fundamental visibility problem in Computational Geometry. The input consists of a simple polygon P , (possibly infinite)...
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A note on starshaped hypersurfaces with almost constant mean curvature in space forms
We show that closed starshaped hypersurfaces of space forms with almost constant mean curvature or almost constant higher order mean curvature are...
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Mean Convex Smoothing of Mean Convex Cones
We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space,...
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Representative Functions, Variational Convergence and Almost Convexity
We develop a new epi-convergence based on the use of bounded convergent nets on the product topology of the strong topology on the primal space and...
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Viscous Approximations of Non-Convex Swee** Processes in the Space of Regulated Functions
Vanishing viscosity approximations are considered here for discontinuous swee** processes with non-convex constraints. It is shown that they are...
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Alexandrov–Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
In this paper, we first introduce quermassintegrals for capillary hypersurfaces in the half-space. Then we solve the related isoperimetric type...
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From valuations on convex bodies to convex functions
A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by...
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Convex Non-convex Variational Models
An important class of computational techniques to solve inverse problems in image processing relies on a variational approach: the optimal output is...
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Convex and non-convex adaptive TV regularizations for color image restoration
Color image restoration is an important and challenging research topic in image processing. Different from grayscale images, each color image has...
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Locally Convex Spaces
This chapter starts recalling the definitions of Hausdorff topological space, metric space, and normed space. Examples of Banach sequence spaces, of...
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Almost Periodic Functions with Values in a Locally Convex Space
Let E = E(τ) be a complete Hausdorff locally convex space. A function...
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Supremum of convex functions
In this chapter, we characterize the subdifferential of pointwise suprema of arbitrarily indexed families of convex functions, defined on a separated...
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Convex Functions
This chapter is devoted to convex functions, the rock star of optimization theory. In this section, we recall their key properties that matter for...
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Chasing Convex Bodies Optimally
In the chasing convex bodies problem, an online player receives a request sequence of N convex sets...