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Weak Solutions to Monge–Ampère Type Equations on Compact Hermitian Manifold with Boundary
We prove the bounded subsolution theorem for the complex Monge–Ampère type equation, with the right-hand side being a positive Radon measure, on a...
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Killing Fields on Compact Pseudo-Kähler Manifolds
We show that a Killing field on a compact pseudo-Kähler ddbar manifold is necessarily (real) holomorphic. Our argument works without the ddbar...
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Differential Structure of Kähler Manifold with Almost Nonnegative Orthogonal Bisectional Curvature
In this short note, we suggest a definition of almost nonnegativity for orthogonal bisectional curvature and quadratic orthogonal bisectional...
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Minimal Euler characteristics of 4-manifolds with 3-manifold groups
Let π = π 1 ( M ) for a compact 3-manifold M , and χ 4 , p and q* be the invariants of Hausmann and Weinberger (1985), Kotschick (1994) and Hillman (2002),...
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Normal and Compact Solvability of the Exterior Derivation Operator in Orlicz Spaces
We study the normal and compact solvability of the operator of exterior derivation in Orlicz spaces of differential forms on compact Riemannian...
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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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Manifold Theory
Curves and surfaces are the fundamental concepts of studying geometry in a 3-dimensional space. The quest for studying these two concepts in a space...
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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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Deformations of Compact Complex Manifolds with Ample Canonical Bundles
In this paper, the author discusses the deformations of compact complex manifolds with ample canonical bundles. It is known that a complex manifold...
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The metric structure of compact rank-one ECS manifolds
Pseudo-Riemannian manifolds with nonzero parallel Weyl tensor which are not locally symmetric are known as ECS manifolds. Every ECS manifold carries...
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Schwarz lemma from a Kähler manifold into a complex Finsler manifold
Suppose that M is a complete Kähler manifold such that its holomorphic sectional curvature is bounded from below by a constant and its radial...
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Diameter of Compact Riemann Surfaces
Diameter is one of the most basic properties of a geometric object, while Riemann surfaces are one of the most basic geometric objects. Surprisingly,...
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Manifold turnpikes of nonlinear port-Hamiltonian descriptor systems under minimal energy supply
Turnpike phenomena of nonlinear port-Hamiltonian descriptor systems under minimal energy supply are studied. Under assumptions on the smoothness of...
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Hermite multiwavelets for manifold-valued data
In this paper we present a construction of interpolatory Hermite multiwavelets for functions that take values in nonlinear geometries such as...
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Generalization of the Notion of Completeness of a Riemannian Analytic Manifold
In this paper, we discuss the concept of an analytic prolongation of a local Riemannian metric. We propose a generalization of the notion of...