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On a Special Map** of a Cone in a Manifold of Bounded Curvature
The aim of the present work is to extend Theorem 1 of the article [4] (Chap. 10 ) by the present author, which...
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Solution to a Two-Dimensional Nonlinear Parabolic Heat Equation Subject to a Boundary Condition Specified on a Moving Manifold
AbstractThis paper is devoted to the study of a degenerating parabolic heat equation with nonlinearities of a general type in the presence of a...
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Holomorphic Retractions of Bounded Symmetric Domains onto Totally Geodesic Complex Submanifolds
Given a bounded symmetric domain Ω the author considers the geometry of its totally geodesic complex submanifolds S ⊂ Ω. In terms of the...
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A Subsolution Theorem for the Monge-Ampère Equation over an Almost Hermitian Manifold
Let Ω ⊆ M be a bounded domain with a smooth boundary ∂Ω, where ( M, J, g ) is a compact, almost Hermitian manifold. The main result of this paper is to...
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Symmetric elastic knots
Minimizing the bending energy within knot classes leads to the concept of elastic knots which has been initiated by von der Mosel (Asymptot Anal...
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The weakly generalized unicorns in Finsler geometry
We classify the almost regular weakly stretch non-Randers-type ( α, β )-metrics with vanishing S-curvature. In the class of regular metrics, they...
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An Averaging Principle for Stochastic Flows and Convergence of Non-Symmetric Dirichlet Forms
We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using...
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m-pseudoconcavity and compactness
The core of a compact set in a general complex manifold has been defined by Shcherbina very recently to study the existence of strictly...
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Trudinger–Moser Inequalities on a Closed Riemann Surface with a Symmetric Conical Metric
This is a continuation of our previous work ( Ann. Sc. Norm. Super. Pisa Cl. Sci. , 20 , 1295–1324, 2020). Let (Σ, g ) be a closed Riemann surface, where...
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Geometry on the Wasserstein Space Over a Compact Riemannian Manifold
We revisit the intrinsic differential geometry of the Wasserstein space over a Riemannian manifold, due to a series of papers by Otto, Otto-Villani,...
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Geometric Flow, Multiplier Ideal Sheaves and Optimal Destabilizer for a Fano Manifold
In (Donaldson in J Differ Geom 70(3):453–472, 2005), it was asked whether the lower bound of the Calabi functional is achieved by a sequence of the...
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Sign-changing solutions for elliptic problem involving the sixth order GJMS operator on compact manifold
In this paper, we use a variational approach due to Yamabe to show the existence of sign-changing solutions to a critical elliptic equation involving...
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Viterbo conjecture for Zoll symmetric spaces
We prove a conjecture of Viterbo from 2007 on the existence of a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the...
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Sobolev Spaces and Laplace Problems on a Riemannian Manifold
With this chapter, our first goal is to give a geometrical definition of Sobolev spaces on a Riemannian manifold, as the norms associated with those...
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RETRACTED ARTICLE: Minimal Period Symmetric Solutions for Some Hamiltonian Systems Via the Nehari Manifold Method
For a given T > 0, we prove, under the global ARS -condition and using the Nehari manifold method, the existence of a T -periodic solution having the W -...
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Proximal Methods Avoid Active Strict Saddles of Weakly Convex Functions
We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on...
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Ancient Solutions of Ricci Flow with Type I Curvature Growth
Ancient solutions of the Ricci flow arise naturally as models for singularity formation. There has been significant progress towards the...