<p>By establishing second main theorems for holomorphic curves from angular domains <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\Omega_{\alpha,\beta}=\{\alpha<\arg z<\beta\}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Ω</mi> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo stretchy="false">{</mo> <mi>α</mi> <mo><</mo> <mo>arg</mo> <mi>z</mi> <mo><</mo> <mi>β</mi> <mo stretchy="false">}</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> into the projective space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathbb{P}^n(\mathbb{C})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>n</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> intersecting families of slowly moving hyperplanes with truncated counting functions, we study the growth of holomorphic curves from <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathbb{C}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> </InlineEquation> into <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathbb{P}^n(\mathbb{C})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>n</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> with radially distributed slowly moving hyperplanes. On the other hand, by establishing some second main theorems on <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$ {\overline{\Omega}}_{\alpha,\beta}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover> <mi mathvariant="normal">Ω</mi> <mo>¯</mo> </mover> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> with Tsuji characteristic function, we give some uniqueness theorems for holomorphic curves from <InlineEquation ID="IEq6"> <EquationSource Format="TEX">${\overline{\Omega}}_{\alpha,\beta}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover> <mi mathvariant="normal">Ω</mi> <mo>¯</mo> </mover> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> into <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\mathbb{P}^n(\mathbb{C})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>n</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> sharing few slowly moving hyperplanes. </p>

Growth of holomorphic curves with radially distributed slowly moving hyperplanes and uniqueness problem

期刊论文
发表日期：

2026年6月19日

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S. D. Quang

摘要

By establishing second main theorems for holomorphic curves from angular domains $\Omega_{\alpha,\beta}=\{\alpha<\arg z<\beta\}$ $Ω_{α, β} = {α < arg z < β}$ into the projective space $\mathbb{P}^n(\mathbb{C})$ $P^{n} (C)$ intersecting families of slowly moving hyperplanes with truncated counting functions, we study the growth of holomorphic curves from $\mathbb{C}$ $C$ into $\mathbb{P}^n(\mathbb{C})$ $P^{n} (C)$ with radially distributed slowly moving hyperplanes. On the other hand, by establishing some second main theorems on $ {\overline{\Omega}}_{\alpha,\beta}$ ${\bar{Ω}}_{α, β}$ with Tsuji characteristic function, we give some uniqueness theorems for holomorphic curves from ${\overline{\Omega}}_{\alpha,\beta}$ ${\bar{Ω}}_{α, β}$ into $\mathbb{P}^n(\mathbb{C})$ $P^{n} (C)$ sharing few slowly moving hyperplanes.